Partial Differential Equations In Fluid Mechanics

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Partial Differential Equations in Fluid Mechanics

Charles L. Fefferman,James C. Robinson,José L. Rodrigo
Partial Differential Equations in Fluid Mechanics Book PDF

Author : Charles L. Fefferman,James C. Robinson,José L. Rodrigo
Publisher : Cambridge University Press
Page : 339 pages
File Size : 52,8 Mb
Release : 2018-09-27
Category : Mathematics
ISBN : 9781108573597

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Partial Differential Equations in Fluid Mechanics by Charles L. Fefferman,James C. Robinson,José L. Rodrigo Pdf

The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.

Partial Differential Equations and Fluid Mechanics

James C. Robinson
Partial Differential Equations and Fluid Mechanics Book PDF

Author : James C. Robinson
Publisher : Cambridge University Press
Page : 270 pages
File Size : 45,7 Mb
Release : 2009-07-16
Category : Mathematics
ISBN : 9780521125123

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Partial Differential Equations and Fluid Mechanics by James C. Robinson Pdf

Reviews and research articles summarizing a wide range of active research topics in fluid mechanics.

Partial Differential Equations in Fluid Dynamics

Isom H. Herron,Michael R. Foster (mathématicien))
Partial Differential Equations in Fluid Dynamics Book PDF

Author : Isom H. Herron,Michael R. Foster (mathématicien))
Publisher : Unknown
Page : 282 pages
File Size : 41,9 Mb
Release : 2008
Category : Differential equations, Partial
ISBN : 0511427557

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Partial Differential Equations in Fluid Dynamics by Isom H. Herron,Michael R. Foster (mathématicien)) Pdf

This book concerns partial differential equations applied to fluids problems in science and engineering.

Partial Differential Equations in Fluid Dynamics

Isom H. Herron,Michael R. Foster
Partial Differential Equations in Fluid Dynamics Book PDF

Author : Isom H. Herron,Michael R. Foster
Publisher : Unknown
Page : 282 pages
File Size : 45,7 Mb
Release : 2008
Category : Mathematics
ISBN : 0511429738

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Partial Differential Equations in Fluid Dynamics by Isom H. Herron,Michael R. Foster Pdf

This book concerns partial differential equations applied to fluids problems in science and engineering.

Energy Methods for Free Boundary Problems

S.N. Antontsev,J.I. Diaz,S. Shmarev
Energy Methods for Free Boundary Problems Book PDF

Author : S.N. Antontsev,J.I. Diaz,S. Shmarev
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,5 Mb
Release : 2001-10-26
Category : Technology & Engineering
ISBN : 0817641238

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Energy Methods for Free Boundary Problems by S.N. Antontsev,J.I. Diaz,S. Shmarev Pdf

For the past several decades, the study of free boundary problems has been a very active subject of research occurring in a variety of applied sciences. What these problems have in common is their formulation in terms of suitably posed initial and boundary value problems for nonlinear partial differential equations. Such problems arise, for example, in the mathematical treatment of the processes of heat conduction, filtration through porous media, flows of non-Newtonian fluids, boundary layers, chemical reactions, semiconductors, and so on. The growing interest in these problems is reflected by the series of meetings held under the title "Free Boundary Problems: Theory and Applications" (Ox ford 1974, Pavia 1979, Durham 1978, Montecatini 1981, Maubuisson 1984, Irsee 1987, Montreal 1990, Toledo 1993, Zakopane 1995, Crete 1997, Chiba 1999). From the proceedings of these meetings, we can learn about the different kinds of mathematical areas that fall within the scope of free boundary problems. It is worth mentioning that the European Science Foundation supported a vast research project on free boundary problems from 1993 until 1999. The recent creation of the specialized journal Interfaces and Free Boundaries: Modeling, Analysis and Computation gives us an idea of the vitality of the subject and its present state of development. This book is a result of collaboration among the authors over the last 15 years.

Large-Scale PDE-Constrained Optimization in Applications

Subhendu Bikash Hazra
Large Scale PDE Constrained Optimization in Applications Book PDF

Author : Subhendu Bikash Hazra
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 53,7 Mb
Release : 2009-12-16
Category : Mathematics
ISBN : 9783642015021

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Large-Scale PDE-Constrained Optimization in Applications by Subhendu Bikash Hazra Pdf

With continuous development of modern computing hardware and applicable - merical methods, computational ?uid dynamics (CFD) has reached certain level of maturity so that it is being used routinely by scientists and engineers for ?uid ?ow analysis. Since most of the real-life applications involve some kind of optimization, it has been natural to extend the use of CFD tools from ?ow simulation to simu- tion based optimization. However, the transition from simulation to optimization is not straight forward, it requires proper interaction between advanced CFD meth- ologies and state-of-the-art optimization algorithms. The ultimate goal is to achieve optimal solution at the cost of few ?ow solutions. There is growing number of - search activities to achieve this goal. This book results from my work done on simulation based optimization problems at the Department of Mathematics, University of Trier, and reported in my postd- toral thesis (”Habilitationsschrift”) accepted by the Faculty-IV of this University in 2008. The focus of the work has been to develop mathematical methods and - gorithms which lead to ef?cient and high performance computational techniques to solve such optimization problems in real-life applications. Systematic development of the methods and algorithms are presented here. Practical aspects of implemen- tions are discussed at each level as the complexity of the problems increase, suppo- ing with enough number of computational examples.

Fundamentals of Computational Fluid Dynamics

H. Lomax,Thomas H. Pulliam,David W. Zingg
Fundamentals of Computational Fluid Dynamics Book PDF

Author : H. Lomax,Thomas H. Pulliam,David W. Zingg
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 47,5 Mb
Release : 2013-03-09
Category : Science
ISBN : 9783662046548

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Fundamentals of Computational Fluid Dynamics by H. Lomax,Thomas H. Pulliam,David W. Zingg Pdf

The chosen semi-discrete approach of a reduction procedure of partial differential equations to ordinary differential equations and finally to difference equations gives the book its distinctiveness and provides a sound basis for a deep understanding of the fundamental concepts in computational fluid dynamics.

Physics and Partial Differential Equations

Tatsien Li,Tiehu Qin
Physics and Partial Differential Equations Book PDF

Author : Tatsien Li,Tiehu Qin
Publisher : SIAM
Page : 274 pages
File Size : 55,9 Mb
Release : 2013-08-14
Category : Mathematics
ISBN : 9781611972276

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Physics and Partial Differential Equations by Tatsien Li,Tiehu Qin Pdf

Now available in English for the first time,?Physics and Partial Differential Equations, Volume I?bridges physics and applied mathematics in a manner that is easily accessible to readers with an undergraduate-level background in these disciplines.? Readers who are more familiar with mathematics than physics will discover the connection between various physical and mechanical disciplines and their related mathematical models, which are described by partial differential equations (PDEs). The authors establish the fundamental equations for fields such as electrodynamics; fluid dynamics, magnetohydrodynamics, and reacting fluid dynamics; elastic, thermoelastic, and viscoelastic mechanics; the kinetic theory of gases; special relativity; and quantum mechanics. Readers who are more familiar with physics than mathematics will benefit from in-depth explanations of how PDEs work as effective mathematical tools to more clearly express and present the basic concepts of physics. The book describes the mathematical structures and features of these PDEs, including the types and basic characteristics of the equations, the behavior of solutions, and some commonly used approaches to solving PDEs. Each chapter can be read independently and includes exercises and references.?

Partial Differential Equations in Mechanics 2

A.P.S. Selvadurai
Partial Differential Equations in Mechanics 2 Book PDF

Author : A.P.S. Selvadurai
Publisher : Springer Science & Business Media
Page : 713 pages
File Size : 52,5 Mb
Release : 2013-06-29
Category : Technology & Engineering
ISBN : 9783662092057

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Partial Differential Equations in Mechanics 2 by A.P.S. Selvadurai Pdf

This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.

Singular Limits in Thermodynamics of Viscous Fluids

Eduard Feireisl,Antonín Novotný
Singular Limits in Thermodynamics of Viscous Fluids Book PDF

Author : Eduard Feireisl,Antonín Novotný
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 42,7 Mb
Release : 2009-03-28
Category : Science
ISBN : 9783764388430

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Singular Limits in Thermodynamics of Viscous Fluids by Eduard Feireisl,Antonín Novotný Pdf

Many interesting problems in mathematical fluid dynamics involve the behavior of solutions of nonlinear systems of partial differential equations as certain parameters vanish or become infinite. Frequently the limiting solution, provided the limit exists, satisfies a qualitatively different system of differential equations. This book is designed as an introduction to the problems involving singular limits based on the concept of weak or variational solutions. The primitive system consists of a complete system of partial differential equations describing the time evolution of the three basic state variables: the density, the velocity, and the absolute temperature associated to a fluid, which is supposed to be compressible, viscous, and heat conducting. It can be represented by the Navier-Stokes-Fourier-system that combines Newton's rheological law for the viscous stress and Fourier's law of heat conduction for the internal energy flux. As a summary, this book studies singular limits of weak solutions to the system governing the flow of thermally conducting compressible viscous fluids.

Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models

Pierre-Louis Lions
Mathematical Topics in Fluid Mechanics Volume 2 Compressible Models Book PDF

Author : Pierre-Louis Lions
Publisher : Oxford University Press
Page : 370 pages
File Size : 52,9 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 0198514883

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Mathematical Topics in Fluid Mechanics: Volume 2: Compressible Models by Pierre-Louis Lions Pdf

Fluid mechanics models consist of systems of nonlinear partial differential equations for which, despite a long history of important mathematical contributions, no complete mathematical understanding is available. The second volume of this book describes compressible fluid-mechanics models. The book contains entirely new material on a subject known to be rather difficult and important for applications (compressible flows). It is probably a unique effort on the mathematical problems associated with the compressible Navier-Stokes equations, written by one of the world's leading experts on nonlinear partial differential equations. Professor P.L. Lions won the Fields Medal in 1994.

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 54,6 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Recent Developments of Mathematical Fluid Mechanics

Herbert Amann,Yoshikazu Giga,Hideo Kozono,Hisashi Okamoto,Masao Yamazaki
Recent Developments of Mathematical Fluid Mechanics Book PDF

Author : Herbert Amann,Yoshikazu Giga,Hideo Kozono,Hisashi Okamoto,Masao Yamazaki
Publisher : Birkhäuser
Page : 482 pages
File Size : 46,7 Mb
Release : 2016-02-28
Category : Mathematics
ISBN : 3034809387

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Recent Developments of Mathematical Fluid Mechanics by Herbert Amann,Yoshikazu Giga,Hideo Kozono,Hisashi Okamoto,Masao Yamazaki Pdf

The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

Nonlinear Partial Differential Equations for Scientists and Engineers

Lokenath Debnath
Nonlinear Partial Differential Equations for Scientists and Engineers Book PDF

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
Page : 602 pages
File Size : 45,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489928467

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Nonlinear Partial Differential Equations for Scientists and Engineers by Lokenath Debnath Pdf

This expanded and revised second edition is a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied applications. Building upon the successful material of the first book, this edition contains updated modern examples and applications from diverse fields. Methods and properties of solutions, along with their physical significance, help make the book more useful for a diverse readership. The book is an exceptionally complete text/reference for graduates, researchers, and professionals in mathematics, physics, and engineering.

Numerical Methods in Fluid Dynamics

Gary A. Sod
Numerical Methods in Fluid Dynamics Book PDF

Author : Gary A. Sod
Publisher : Cambridge University Press
Page : 464 pages
File Size : 54,8 Mb
Release : 1985-10-31
Category : Mathematics
ISBN : 052125924X

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Numerical Methods in Fluid Dynamics by Gary A. Sod Pdf

Here is an introduction to numerical methods for partial differential equations with particular reference to those that are of importance in fluid dynamics. The author gives a thorough and rigorous treatment of the techniques, beginning with the classical methods and leading to a discussion of modern developments. For easier reading and use, many of the purely technical results and theorems are given separately from the main body of the text. The presentation is intended for graduate students in applied mathematics, engineering and physical sciences who have a basic knowledge of partial differential equations.