Existence Theory For Generalized Newtonian Fluids
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Existence Theory For Generalized Newtonian Fluids
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Author : Dominic Breit
language : en
Publisher: Academic Press
Release Date : 2017-03-22
Existence Theory For Generalized Newtonian Fluids written by Dominic Breit and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-22 with Mathematics categories.
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
Variational Methods For Problems From Plasticity Theory And For Generalized Newtonian Fluids
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Author : Martin Fuchs
language : en
Publisher: Springer
Release Date : 2007-05-06
Variational Methods For Problems From Plasticity Theory And For Generalized Newtonian Fluids written by Martin Fuchs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
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.
Topics In Mathematical Fluid Mechanics
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Author : Peter Constantin
language : en
Publisher: Springer
Release Date : 2013-04-03
Topics In Mathematical Fluid Mechanics written by Peter Constantin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-03 with Mathematics categories.
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.
Recent Advances In Partial Differential Equations And Applications
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Author : Vicenţiu D. Rădulescu
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-06-28
Recent Advances In Partial Differential Equations And Applications written by Vicenţiu D. Rădulescu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-28 with Mathematics categories.
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.
Pseudo Monotone Operator Theory For Unsteady Problems With Variable Exponents
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Author : Alex Kaltenbach
language : en
Publisher: Springer Nature
Release Date : 2023-09-12
Pseudo Monotone Operator Theory For Unsteady Problems With Variable Exponents written by Alex Kaltenbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-12 with Mathematics categories.
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.
New Trends And Results In Mathematical Description Of Fluid Flows
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Author : Miroslav Bulíček
language : en
Publisher: Springer
Release Date : 2018-09-26
New Trends And Results In Mathematical Description Of Fluid Flows written by Miroslav Bulíček and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-26 with Mathematics categories.
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.
Three Dimensional Navier Stokes Equations For Turbulence
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Author : Luigi C. Berselli
language : en
Publisher: Academic Press
Release Date : 2021-03-10
Three Dimensional Navier Stokes Equations For Turbulence written by Luigi C. Berselli and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Science categories.
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
Nonlinear Elliptic And Parabolic Problems
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Author : Michel Chipot
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-10-18
Nonlinear Elliptic And Parabolic Problems written by Michel Chipot and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-10-18 with Mathematics categories.
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.
Mathematical Aspects Of Fluid Mechanics
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Author : James C. Robinson
language : en
Publisher: Cambridge University Press
Release Date : 2012-10-18
Mathematical Aspects Of Fluid Mechanics written by James C. Robinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-18 with Mathematics categories.
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.
Rheology And Non Newtonian Fluids
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Author : Fridtjov Irgens
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-25
Rheology And Non Newtonian Fluids written by Fridtjov Irgens and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-25 with Technology & Engineering categories.
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