Existence Theory For Generalized Newtonian Fluids

Author : Dominic Breit
Publisher : Academic Press
Page : 286 pages
File Size : 54,7 Mb
Release : 2017-03-22
Category : Mathematics
ISBN : 9780128110454

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Existence Theory for Generalized Newtonian Fluids by Dominic Breit Pdf

Existence Theory for Generalized Newtonian Fluids provides a rigorous mathematical treatment of the existence of weak solutions to generalized Navier-Stokes equations modeling Non-Newtonian fluid flows. The book presents classical results, developments over the last 50 years of research, and recent results with proofs. Provides the state-of-the-art of the mathematical theory of Generalized Newtonian fluids Combines elliptic, parabolic and stochastic problems within existence theory under one umbrella Focuses on the construction of the solenoidal Lipschitz truncation, thus enabling readers to apply it to mathematical research Approaches stochastic PDEs with a perspective uniquely suitable for analysis, providing an introduction to Galerkin method for SPDEs and tools for compactness

Author : Martin Fuchs,Gregory Seregin
Publisher : Springer
Page : 276 pages
File Size : 45,5 Mb
Release : 2007-05-06
Category : Mathematics
ISBN : 9783540444428

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Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids by Martin Fuchs,Gregory Seregin Pdf

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

Author : Martin Sauer
Publisher : Unknown
Page : 138 pages
File Size : 51,7 Mb
Release : 2013
Category : Electronic
ISBN : 3843909563

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Existence and Uniqueness Results for Randomly Forced Generalized Newtonian Fluids by Martin Sauer Pdf

Author : Vicenţiu D. Rădulescu,Adélia Sequeira,Vsevolod A. Solonnikov
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 54,7 Mb
Release : 2016-06-28
Category : Differential equations, Partial
ISBN : 9781470415211

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Recent Advances in Partial Differential Equations and Applications by Vicenţiu D. Rădulescu,Adélia Sequeira,Vsevolod A. Solonnikov Pdf

This volume contains the proceedings of the International Conference on Recent Advances in PDEs and Applications, in honor of Hugo Beirão da Veiga's 70th birthday, held from February 17–21, 2014, in Levico Terme, Italy. The conference brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants. The workshop program testified to the wide-ranging influence of Hugo Beirão da Veiga on the field of partial differential equations, in particular those related to fluid dynamics. In his own work, da Veiga has been a seminal influence in many important areas: Navier-Stokes equations, Stokes systems, non-Newtonian fluids, Euler equations, regularity of solutions, perturbation theory, vorticity phenomena, and nonlinear potential theory, as well as various degenerate or singular models in mathematical physics. This same breadth is reflected in the mathematical papers included in this volume.

Author : Alex Kaltenbach
Publisher : Springer Nature
Page : 364 pages
File Size : 42,7 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.

Author : Miroslav Bulíček,Eduard Feireisl,Milan Pokorný
Publisher : Springer
Page : 190 pages
File Size : 52,9 Mb
Release : 2018-09-26
Category : Mathematics
ISBN : 9783319943435

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New Trends and Results in Mathematical Description of Fluid Flows by Miroslav Bulíček,Eduard Feireisl,Milan Pokorný Pdf

The book presents recent results and new trends in the theory of fluid mechanics. Each of the four chapters focuses on a different problem in fluid flow accompanied by an overview of available older results. The chapters are extended lecture notes from the ESSAM school "Mathematical Aspects of Fluid Flows" held in Kácov (Czech Republic) in May/June 2017. The lectures were presented by Dominic Breit (Heriot-Watt University Edinburgh), Yann Brenier (École Polytechnique, Palaiseau), Pierre-Emmanuel Jabin (University of Maryland) and Christian Rohde (Universität Stuttgart), and cover various aspects of mathematical fluid mechanics – from Euler equations, compressible Navier-Stokes equations and stochastic equations in fluid mechanics to equations describing two-phase flow; from the modeling and mathematical analysis of equations to numerical methods. Although the chapters feature relatively recent results, they are presented in a form accessible to PhD students in the field of mathematical fluid mechanics.

Author : Luigi C. Berselli
Publisher : Academic Press
Page : 330 pages
File Size : 46,6 Mb
Release : 2021-03-10
Category : Science
ISBN : 9780128219454

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Three-Dimensional Navier-Stokes Equations for Turbulence by Luigi C. Berselli Pdf

Three-Dimensional Navier-Stokes Equations for Turbulence provides a rigorous but still accessible account of research into local and global energy dissipation, with particular emphasis on turbulence modeling. The mathematical detail is combined with coverage of physical terms such as energy balance and turbulence to make sure the reader is always in touch with the physical context. All important recent advancements in the analysis of the equations, such as rigorous bounds on structure functions and energy transfer rates in weak solutions, are addressed, and connections are made to numerical methods with many practical applications. The book is written to make this subject accessible to a range of readers, carefully tackling interdisciplinary topics where the combination of theory, numerics, and modeling can be a challenge. Includes a comprehensive survey of modern reduced-order models, including ones for data assimilation Includes a self-contained coverage of mathematical analysis of fluid flows, which will act as an ideal introduction to the book for readers without mathematical backgrounds Presents methods and techniques in a practical way so they can be rapidly applied to the reader’s own work

Author : Peter Constantin,Arnaud Debussche,Giovanni P. Galdi,Michael Růžička,Gregory Seregin
Publisher : Springer
Page : 323 pages
File Size : 50,8 Mb
Release : 2013-04-03
Category : Mathematics
ISBN : 9783642362972

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Topics in Mathematical Fluid Mechanics by Peter Constantin,Arnaud Debussche,Giovanni P. Galdi,Michael Růžička,Gregory Seregin Pdf

This volume brings together five contributions to mathematical fluid mechanics, a classical but still very active research field which overlaps with physics and engineering. The contributions cover not only the classical Navier-Stokes equations for an incompressible Newtonian fluid, but also generalized Newtonian fluids, fluids interacting with particles and with solids, and stochastic models. The questions addressed in the lectures range from the basic problems of existence of weak and more regular solutions, the local regularity theory and analysis of potential singularities, qualitative and quantitative results about the behavior in special cases, asymptotic behavior, statistical properties and ergodicity.

Author : Fridtjov Irgens
Publisher : Springer Science & Business Media
Page : 190 pages
File Size : 54,9 Mb
Release : 2013-07-25
Category : Technology & Engineering
ISBN : 9783319010533

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Rheology and Non-Newtonian Fluids by Fridtjov Irgens Pdf

This book gives a brief but thorough introduction to the fascinating subject of non-Newtonian fluids, their behavior and mechanical properties. After a brief introduction of what characterizes non-Newtonian fluids in Chapter 1 some phenomena characteristic of non-Newtonian fluids are presented in Chapter 2. The basic equations in fluid mechanics are discussed in Chapter 3. Deformation kinematics, the kinematics of shear flows, viscometric flows, and extensional flows are the topics in Chapter 4. Material functions characterizing the behavior of fluids in special flows are defined in Chapter 5. Generalized Newtonian fluids are the most common types of non-Newtonian fluids and are the subject in Chapter 6. Some linearly viscoelastic fluid models are presented in Chapter 7. In Chapter 8 the concept of tensors is utilized and advanced fluid models are introduced. The book is concluded with a variety of 26 problems. Solutions to the problems are ready for instructors

Author : Michel Chipot
Publisher : Springer Science & Business Media
Page : 556 pages
File Size : 49,8 Mb
Release : 2005-10-18
Category : Mathematics
ISBN : 3764372664

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Nonlinear Elliptic and Parabolic Problems by Michel Chipot Pdf

The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.

Author : J. Necas,J. Malek,M. Rokyta,M. Ruzicka
Publisher : CRC Press
Page : 334 pages
File Size : 42,7 Mb
Release : 2019-08-16
Category : Mathematics
ISBN : 9781000723120

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Weak and Measure-Valued Solutions to Evolutionary PDEs by J. Necas,J. Malek,M. Rokyta,M. Ruzicka Pdf

This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering

Author : Boling Guo,Chunxiao Guo,Yaqing Liu,Qiaoxin Li
Publisher : Walter de Gruyter GmbH & Co KG
Page : 350 pages
File Size : 52,7 Mb
Release : 2018-10-08
Category : Mathematics
ISBN : 9783110549409

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Non-Newtonian Fluids by Boling Guo,Chunxiao Guo,Yaqing Liu,Qiaoxin Li Pdf

This book provides an up-to-date overview of mathematical theories and research results in non-Newtonian fluid dynamics. Related mathematical models, solutions as well as numerical experiments are discussed. Fundamental theories and practical applications make it a handy reference for researchers and graduate students in mathematics, physics and engineering. Contents Non-Newtonian fluids and their mathematical model Global solutions to the equations of non-Newtonian fluids Global attractors of incompressible non-Newtonian fluids Global attractors of modified Boussinesq approximation Inertial manifolds of incompressible non-Newtonian fluids The regularity of solutions and related problems Global attractors and time-spatial chaos Non-Newtonian generalized fluid and their applications

Author : Bernard D. Coleman,Hershel Markovitz,W. Noll
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642886553

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Viscometric Flows of Non-Newtonian Fluids by Bernard D. Coleman,Hershel Markovitz,W. Noll Pdf

We here attempt to give a complete but concise treatment of the theory of steady viscometric flows of simple (non-Newtonian) fluids and to use that theory to discuss the design and interpretation of ex periments. We are able to present the theory with less mathematical machinery than was used in our original papers, partly because this Tract has more limited aims than those papers, and partly because we employ a method, found by Noll and published here for the first time, for dealing with visco metric flows without the apparatus of rela tive Cauchy-Green tensors and reduced constitutive equations. To make the theory accessible to students not familiar with modern mathematics, we have added to our Tract an appendix explaining some of the mathe matical concepts essential to continuum physics. Pittsburgh, July 1965 BERNARD D. COLEMAN HERSHEL MARKOVITZ WALTER NOLL CONTENTS I. Introduction page 1. Limitations of the Classical Theory of Navier and Stokes. 1 5 2. Incompressible Simple Fluids. . . . . . . . . . . . 3. Plan and Scope of this Monograph . . . . . . . . . 7 II. Theory of Incompressible Simple Fluids 4. Kinematics. . . . . . . . . . . . 10 5. The Dynamical Equations . . . . . . . . . . . 12 6. The Principle of Material Objectivity . . . . . . 14 7. The Definition of an Incompressible Simple Fluid . 17 8. Static Behavior of Simple Fluids . . . . . . . . 19 III. General Theory of Viscometric Flows 9. The Kinematics of Simple Shearing Flow 21 10. The Viscometric Functions . . . . . . . . . . 22 11. The Dynamics of Simple Shearing Flow; Viscosity 26 12. The Definition of a Viscometric Flow 29 13. Curvilineal Flows. . . . . . . . 30 1. Kinematical Description . . . .

Author : Michael Renardy
Publisher : SIAM
Page : 113 pages
File Size : 44,9 Mb
Release : 2000-01-01
Category : Mathematics
ISBN : 0898719410

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Mathematical Analysis of Viscoelastic Flows by Michael Renardy Pdf

This monograph is based on a series of lectures presented at the 1999 NSF-CBMS Regional Research Conference on Mathematical Analysis of Viscoelastic Flows. It begins with an introduction to phenomena observed in viscoelastic flows, the formulation of mathematical equations to model such flows, and the behavior of various models in simple flows. It also discusses the asymptotics of the high Weissenberg limit, the analysis of flow instabilities, the equations of viscoelastic flows, jets and filaments and their breakup, as well as several other topics.

Author : James C. Robinson,José L. Rodrigo,Witold Sadowski
Publisher : Cambridge University Press
Page : 275 pages
File Size : 48,5 Mb
Release : 2012-10-18
Category : Mathematics
ISBN : 9781139577212

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Mathematical Aspects of Fluid Mechanics by James C. Robinson,José L. Rodrigo,Witold Sadowski Pdf

The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.