Mathematical Tools For The Study Of The Incompressible Navier Stokes Equations And Related Models

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Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models

Franck Boyer,Pierre Fabrie
Mathematical Tools for the Study of the Incompressible Navier Stokes Equations andRelated Models Book PDF

Author : Franck Boyer,Pierre Fabrie
Publisher : Springer Science & Business Media
Page : 538 pages
File Size : 40,5 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 9781461459750

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Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models by Franck Boyer,Pierre Fabrie Pdf

The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .

Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models

Franck Boyer,Pierre Fabrie
Mathematical Tools for the Study of the Incompressible Navier Stokes Equations and Related Models Book PDF

Author : Franck Boyer,Pierre Fabrie
Publisher : Springer
Page : 526 pages
File Size : 40,7 Mb
Release : 2012-11-06
Category : Mathematics
ISBN : 1461459761

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Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models by Franck Boyer,Pierre Fabrie Pdf

The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning the Navier-Stokes equations which is the basic model for the flow of incompressible viscous fluids. Authors introduce mathematical tools so that the reader is able to use them for studying many other kinds of partial differential equations, in particular nonlinear evolution problems. The background needed are basic results in calculus, integration, and functional analysis. Some sections certainly contain more advanced topics than others. Nevertheless, the authors’ aim is that graduate or PhD students, as well as researchers who are not specialized in nonlinear analysis or in mathematical fluid mechanics, can find a detailed introduction to this subject. .

An Introduction to the Mathematical Theory of the Navier-Stokes Equations

Giovanni Galdi
An Introduction to the Mathematical Theory of the Navier Stokes Equations Book PDF

Author : Giovanni Galdi
Publisher : Springer Science & Business Media
Page : 1026 pages
File Size : 44,7 Mb
Release : 2011-07-12
Category : Mathematics
ISBN : 9780387096209

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An Introduction to the Mathematical Theory of the Navier-Stokes Equations by Giovanni Galdi Pdf

The book provides a comprehensive, detailed and self-contained treatment of the fundamental mathematical properties of boundary-value problems related to the Navier-Stokes equations. These properties include existence, uniqueness and regularity of solutions in bounded as well as unbounded domains. Whenever the domain is unbounded, the asymptotic behavior of solutions is also investigated. This book is the new edition of the original two volume book, under the same title, published in 1994. In this new edition, the two volumes have merged into one and two more chapters on steady generalized oseen flow in exterior domains and steady Navier–Stokes flow in three-dimensional exterior domains have been added. Most of the proofs given in the previous edition were also updated. An introductory first chapter describes all relevant questions treated in the book and lists and motivates a number of significant and still open questions. It is written in an expository style so as to be accessible also to non-specialists.Each chapter is preceded by a substantial, preliminary discussion of the problems treated, along with their motivation and the strategy used to solve them. Also, each chapter ends with a section dedicated to alternative approaches and procedures, as well as historical notes. The book contains more than 400 stimulating exercises, at different levels of difficulty, that will help the junior researcher and the graduate student to gradually become accustomed with the subject. Finally, the book is endowed with a vast bibliography that includes more than 500 items. Each item brings a reference to the section of the book where it is cited. The book will be useful to researchers and graduate students in mathematics in particular mathematical fluid mechanics and differential equations. Review of First Edition, First Volume: “The emphasis of this book is on an introduction to the mathematical theory of the stationary Navier-Stokes equations. It is written in the style of a textbook and is essentially self-contained. The problems are presented clearly and in an accessible manner. Every chapter begins with a good introductory discussion of the problems considered, and ends with interesting notes on different approaches developed in the literature. Further, stimulating exercises are proposed. (Mathematical Reviews, 1995)

Mathematical and Numerical Foundations of Turbulence Models and Applications

Tomás Chacón Rebollo,Roger Lewandowski
Mathematical and Numerical Foundations of Turbulence Models and Applications Book PDF

Author : Tomás Chacón Rebollo,Roger Lewandowski
Publisher : Springer
Page : 530 pages
File Size : 48,8 Mb
Release : 2014-06-17
Category : Mathematics
ISBN : 9781493904556

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Mathematical and Numerical Foundations of Turbulence Models and Applications by Tomás Chacón Rebollo,Roger Lewandowski Pdf

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

Mathematical Modelling, Applied Analysis and Computation

Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Mathematical Modelling Applied Analysis and Computation Book PDF

Author : Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit
Publisher : Springer Nature
Page : 311 pages
File Size : 40,6 Mb
Release : 2019-08-31
Category : Mathematics
ISBN : 9789811396083

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Mathematical Modelling, Applied Analysis and Computation by Jagdev Singh,Devendra Kumar,Hemen Dutta,Dumitru Baleanu,Sunil Dutt Purohit Pdf

This book contains original research papers presented at the International Conference on Mathematical Modelling, Applied Analysis and Computation, held at JECRC University, Jaipur, India, on 6-8 July, 2018. Organized into 20 chapters, the book focuses on theoretical and applied aspects of various types of mathematical modelling such as equations of various types, fuzzy mathematical models, automata, Petri nets and bond graphs for systems of dynamic nature and the usage of numerical techniques in handling modern problems of science, engineering and finance. It covers the applications of mathematical modelling in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science and finance. A wide variety of dynamical systems like deterministic, stochastic, continuous, discrete or hybrid, with respect to time, are discussed in the book. It provides the mathematical modelling of various problems arising in science and engineering, and also new efficient numerical approaches for solving linear and nonlinear problems and rigorous mathematical theories, which can be used to analyze a different kind of mathematical models. The conference was aimed at fostering cooperation among students and researchers in areas of applied analysis, engineering and computation with the deliberations to inculcate new research ideas in their relevant fields. This volume will provide a comprehensive introduction to recent theories and applications of mathematical modelling and numerical simulation, which will be a valuable resource for graduate students and researchers of mathematical modelling and industrial mathematics.

Interfaces: Modeling, Analysis, Numerics

Eberhard Bänsch,Klaus Deckelnick,Harald Garcke,Paola Pozzi
Interfaces Modeling Analysis Numerics Book PDF

Author : Eberhard Bänsch,Klaus Deckelnick,Harald Garcke,Paola Pozzi
Publisher : Springer Nature
Page : 186 pages
File Size : 52,8 Mb
Release : 2023-11-11
Category : Mathematics
ISBN : 9783031355509

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Interfaces: Modeling, Analysis, Numerics by Eberhard Bänsch,Klaus Deckelnick,Harald Garcke,Paola Pozzi Pdf

These lecture notes are dedicated to the mathematical modelling, analysis and computation of interfaces and free boundary problems appearing in geometry and in various applications, ranging from crystal growth, tumour growth, biological membranes to porous media, two-phase flows, fluid-structure interactions, and shape optimization. We first give an introduction to classical methods from differential geometry and systematically derive the governing equations from physical principles. Then we will analyse parametric approaches to interface evolution problems and derive numerical methods which will be thoroughly analysed. In addition, implicit descriptions of interfaces such as phase field and level set methods will be analysed. Finally, we will discuss numerical methods for complex interface evolutions and will focus on two phase flow problems as an important example of such evolutions.

Parabolic Equations with Irregular Data and Related Issues

Claude Le Bris,Pierre-Louis Lions
Parabolic Equations with Irregular Data and Related Issues Book PDF

Author : Claude Le Bris,Pierre-Louis Lions
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 46,7 Mb
Release : 2019-06-17
Category : Mathematics
ISBN : 9783110635508

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Parabolic Equations with Irregular Data and Related Issues by Claude Le Bris,Pierre-Louis Lions Pdf

This book studies the existence and uniqueness of solutions to parabolic-type equations with irregular coefficients and/or initial conditions. It elaborates on the DiPerna-Lions theory of renormalized solutions to linear transport equations and related equations, and also examines the connection between the results on the partial differential equation and the well-posedness of the underlying stochastic/ordinary differential equation.

The Application of Mathematics to Physics and Nonlinear Science

Andrei Ludu
The Application of Mathematics to Physics and Nonlinear Science Book PDF

Author : Andrei Ludu
Publisher : MDPI
Page : 122 pages
File Size : 49,5 Mb
Release : 2020-04-16
Category : Mathematics
ISBN : 9783039287260

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The Application of Mathematics to Physics and Nonlinear Science by Andrei Ludu Pdf

Nonlinear science is the science of, among other exotic phenomena, unexpected and unpredictable behavior, catastrophes, complex interactions, and significant perturbations. Ocean and atmosphere dynamics, weather, many bodies in interaction, ultra-high intensity excitations, life, formation of natural patterns, and coupled interactions between components or different scales are only a few examples of systems where nonlinear science is necessary. All outstanding, self-sustained, and stable structures in space and time exist and protrude out of a regular linear background of states mainly because they identify themselves from the rest by being highly localized in range, time, configuration, states, and phase spaces. Guessing how high up you drive toward the top of the mountain by compiling your speed, road slope, and trip duration is a linear model, but predicting the occurrence around a turn of a boulder fallen on the road is a nonlinear phenomenon. In an effort to grasp and understand nonlinear phenomena, scientists have developed several mathematical approaches including inverse scattering theory, Backlund and groups of transformations, bilinear method, and several other detailed technical procedures. In this Special Issue, we introduce a few very recent approaches together with their physical meaning and applications. We present here five important papers on waves, unsteady flows, phases separation, ocean dynamics, nonlinear optic, viral dynamics, and the self-appearance of patterns for spatially extended systems, which are problems that have aroused scientists’ interest for decades, yet still cannot be predicted and have their generating mechanism and stability open to debate. The aim of this Special Issue was to present these most debated and interesting topics from nonlinear science for which, despite the existence of highly developed mathematical tools of investigation, there are still fundamental open questions.

Partial Differential Equations and Applications

Toka Diagana,Khalil Ezzinbi,Stanislas Ouaro
Partial Differential Equations and Applications Book PDF

Author : Toka Diagana,Khalil Ezzinbi,Stanislas Ouaro
Publisher : Springer Nature
Page : 351 pages
File Size : 41,9 Mb
Release : 2023-05-11
Category : Mathematics
ISBN : 9783031276613

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Partial Differential Equations and Applications by Toka Diagana,Khalil Ezzinbi,Stanislas Ouaro Pdf

This volume convenes selected, peer-reviewed works presented at the Partial Differential Equations and Applications Colloquium in Honor of Prof. Hamidou Toure that was held at the University Ouaga 1, Ouagadougou, Burkina Faso, November 5–9, 2018. Topics covered in this volume include boundary value problems for difference equations, differential forms in global analysis, functional differential equations, and stability in the context of PDEs. Studies on SIR and SIRS epidemic models, of special interest to researchers in epidemiology, are also included. This volume is dedicated to Dr. Hamidou Touré, a Research Professor at the University of Ouaga 1. Dr. Touré has made important scientific contributions in many fields of mathematical sciences. Dr. Touré got his PhD (1994) from the University of Franche-Comté of Besançon, France, and is one of the key leaders and mentor of several generations of mathematicians in French-speaking Africa. This conference was purposely held in Ouagadougou in reverence of Dr. Touré's efforts for the development of mathematics in Africa since the beginning of his career in early 1982 to the current days.

Fractional Partial Differential Equations

Yong Zhou
Fractional Partial Differential Equations Book PDF

Author : Yong Zhou
Publisher : World Scientific
Page : 319 pages
File Size : 43,5 Mb
Release : 2024-03-12
Category : Mathematics
ISBN : 9789811290428

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Fractional Partial Differential Equations by Yong Zhou Pdf

This monograph offers a comprehensive exposition of the theory surrounding time-fractional partial differential equations, featuring recent advancements in fundamental techniques and results. The topics covered encompass crucial aspects of the theory, such as well-posedness, regularity, approximation, and optimal control. The book delves into the intricacies of fractional Navier-Stokes equations, fractional Rayleigh-Stokes equations, fractional Fokker-Planck equations, and fractional Schrödinger equations, providing a thorough exploration of these subjects. Numerous real-world applications associated with these equations are meticulously examined, enhancing the practical relevance of the presented concepts.The content in this monograph is based on the research works carried out by the author and other excellent experts during the past five years. Rooted in the latest advancements, it not only serves as a valuable resource for understanding the theoretical foundations but also lays the groundwork for delving deeper into the subject and navigating the extensive research landscape. Geared towards researchers, graduate students, and PhD scholars specializing in differential equations, applied analysis, and related research domains, this monograph facilitates a nuanced understanding of time-fractional partial differential equations and their broader implications.

Nonlinear, Nonlocal and Fractional Turbulence

Peter William Egolf,Kolumban Hutter
Nonlinear Nonlocal and Fractional Turbulence Book PDF

Author : Peter William Egolf,Kolumban Hutter
Publisher : Springer Nature
Page : 487 pages
File Size : 53,6 Mb
Release : 2020-04-02
Category : Science
ISBN : 9783030260330

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Nonlinear, Nonlocal and Fractional Turbulence by Peter William Egolf,Kolumban Hutter Pdf

Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new ‘law of the wall’ and a generalization of Kraichnan’s energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.

Computational Science – ICCS 2020

Valeria V. Krzhizhanovskaya,Gábor Závodszky,Michael H. Lees,Jack J. Dongarra,Peter M. A. Sloot,Sérgio Brissos,João Teixeira
Computational Science ICCS 2020 Book PDF

Author : Valeria V. Krzhizhanovskaya,Gábor Závodszky,Michael H. Lees,Jack J. Dongarra,Peter M. A. Sloot,Sérgio Brissos,João Teixeira
Publisher : Springer Nature
Page : 726 pages
File Size : 46,6 Mb
Release : 2020-06-18
Category : Computers
ISBN : 9783030503710

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Computational Science – ICCS 2020 by Valeria V. Krzhizhanovskaya,Gábor Závodszky,Michael H. Lees,Jack J. Dongarra,Peter M. A. Sloot,Sérgio Brissos,João Teixeira Pdf

The seven-volume set LNCS 12137, 12138, 12139, 12140, 12141, 12142, and 12143 constitutes the proceedings of the 20th International Conference on Computational Science, ICCS 2020, held in Amsterdam, The Netherlands, in June 2020.* The total of 101 papers and 248 workshop papers presented in this book set were carefully reviewed and selected from 719 submissions (230 submissions to the main track and 489 submissions to the workshops). The papers were organized in topical sections named: Part I: ICCS Main Track Part II: ICCS Main Track Part III: Advances in High-Performance Computational Earth Sciences: Applications and Frameworks; Agent-Based Simulations, Adaptive Algorithms and Solvers; Applications of Computational Methods in Artificial Intelligence and Machine Learning; Biomedical and Bioinformatics Challenges for Computer Science Part IV: Classifier Learning from Difficult Data; Complex Social Systems through the Lens of Computational Science; Computational Health; Computational Methods for Emerging Problems in (Dis-)Information Analysis Part V: Computational Optimization, Modelling and Simulation; Computational Science in IoT and Smart Systems; Computer Graphics, Image Processing and Artificial Intelligence Part VI: Data Driven Computational Sciences; Machine Learning and Data Assimilation for Dynamical Systems; Meshfree Methods in Computational Sciences; Multiscale Modelling and Simulation; Quantum Computing Workshop Part VII: Simulations of Flow and Transport: Modeling, Algorithms and Computation; Smart Systems: Bringing Together Computer Vision, Sensor Networks and Machine Learning; Software Engineering for Computational Science; Solving Problems with Uncertainties; Teaching Computational Science; UNcErtainty QUantIficatiOn for ComputationAl modeLs *The conference was canceled due to the COVID-19 pandemic.

Crowd Dynamics, Volume 1

Livio Gibelli,Nicola Bellomo
Crowd Dynamics Volume 1 Book PDF

Author : Livio Gibelli,Nicola Bellomo
Publisher : Springer
Page : 292 pages
File Size : 49,8 Mb
Release : 2019-01-22
Category : Mathematics
ISBN : 9783030051297

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Crowd Dynamics, Volume 1 by Livio Gibelli,Nicola Bellomo Pdf

This volume explores the complex problems that arise in the modeling and simulation of crowd dynamics in order to present the state-of-the-art of this emerging field and contribute to future research activities. Experts in various areas apply their unique perspectives to specific aspects of crowd dynamics, covering the topic from multiple angles. These include a demonstration of how virtual reality may solve dilemmas in collecting empirical data; a detailed study on pedestrian movement in smoke-filled environments; a presentation of one-dimensional conservation laws with point constraints on the flux; a collection of new ideas on the modeling of crowd dynamics at the microscopic scale; and others. Applied mathematicians interested in crowd dynamics, pedestrian movement, traffic flow modeling, urban planning, and other topics will find this volume a valuable resource. Additionally, researchers in social psychology, architecture, and engineering may find this information relevant to their work.

Complex fluids

Pierre Saramito
Complex fluids Book PDF

Author : Pierre Saramito
Publisher : Springer
Page : 276 pages
File Size : 40,8 Mb
Release : 2016-10-26
Category : Mathematics
ISBN : 9783319443621

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Complex fluids by Pierre Saramito Pdf

This book presents a comprehensive overview of the modeling of complex fluids, including many common substances, such as toothpaste, hair gel, mayonnaise, liquid foam, cement and blood, which cannot be described by Navier-Stokes equations. It also offers an up-to-date mathematical and numerical analysis of the corresponding equations, as well as several practical numerical algorithms and software solutions for the approximation of the solutions. It discusses industrial (molten plastics, forming process), geophysical (mud flows, volcanic lava, glaciers and snow avalanches), and biological (blood flows, tissues) modeling applications. This book is a valuable resource for undergraduate students and researchers in applied mathematics, mechanical engineering and physics.

Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents

Alex Kaltenbach
Pseudo Monotone Operator Theory for Unsteady Problems with Variable Exponents Book PDF

Author : Alex Kaltenbach
Publisher : Springer Nature
Page : 364 pages
File Size : 41,8 Mb
Release : 2023-09-12
Category : Mathematics
ISBN : 9783031296703

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Pseudo-Monotone Operator Theory for Unsteady Problems with Variable Exponents by Alex Kaltenbach Pdf

This book provides a comprehensive analysis of the existence of weak solutions of unsteady problems with variable exponents. The central motivation is the weak solvability of the unsteady p(.,.)-Navier–Stokes equations describing the motion of an incompressible electro-rheological fluid. Due to the variable dependence of the power-law index p(.,.) in this system, the classical weak existence analysis based on the pseudo-monotone operator theory in the framework of Bochner–Lebesgue spaces is not applicable. As a substitute for Bochner–Lebesgue spaces, variable Bochner–Lebesgue spaces are introduced and analyzed. In the mathematical framework of this substitute, the theory of pseudo-monotone operators is extended to unsteady problems with variable exponents, leading to the weak solvability of the unsteady p(.,.)-Navier–Stokes equations under general assumptions. Aimed primarily at graduate readers, the book develops the material step-by-step, starting with the basics of PDE theory and non-linear functional analysis. The concise introductions at the beginning of each chapter, together with illustrative examples, graphics, detailed derivations of all results and a short summary of the functional analytic prerequisites, will ease newcomers into the subject.