Singular Limits In Thermodynamics Of Viscous Fluids
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Singular Limits In Thermodynamics Of Viscous Fluids
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Author : Eduard Feireisl
language : en
Publisher: Birkhäuser
Release Date : 2017-11-24
Singular Limits In Thermodynamics Of Viscous Fluids written by Eduard Feireisl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-24 with Mathematics categories.
This book is about singular limits of systems of partial differential equations governing the motion of thermally conducting compressible viscous fluids. "The main aim is to provide mathematically rigorous arguments how to get from the compressible Navier-Stokes-Fourier system several less complex systems of partial differential equations used e.g. in meteorology or astrophysics. However, the book contains also a detailed introduction to the modelling in mechanics and thermodynamics of fluids from the viewpoint of continuum physics. The book is very interesting and important. It can be recommended not only to specialists in the field, but it can also be used for doctoral students and young researches who want to start to work in the mathematical theory of compressible fluids and their asymptotic limits." Milan Pokorný (zbMATH) "This book is of the highest quality from every point of view. It presents, in a unified way, recent research material of fundament al importance. It is self-contained, thanks to Chapter 3 (existence theory) and to the appendices. It is extremely well organized, and very well written. It is a landmark for researchers in mathematical fluid dynamics, especially those interested in the physical meaning of the equations and statements." Denis Serre (MathSciNet)
Singular Limits In Thermodynamics Of Viscous Fluids
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Author : John G. Heywood Edited by Giovanni P. Galdi (Rolf Rannacher)
language : en
Publisher:
Release Date : 2009
Singular Limits In Thermodynamics Of Viscous Fluids written by John G. Heywood Edited by Giovanni P. Galdi (Rolf Rannacher) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with categories.
Singular Limits In Thermodynamics Of Viscous Fluids
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Author : Eduard Feireisl
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-28
Singular Limits In Thermodynamics Of Viscous Fluids written by Eduard Feireisl 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 2009-03-28 with Science categories.
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.
New Directions In Mathematical Fluid Mechanics
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Author : Andrei V. Fursikov
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-11
New Directions In Mathematical Fluid Mechanics written by Andrei V. Fursikov 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 2010-01-11 with Science categories.
On November 3, 2005, Alexander Vasil’evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov’s contributions to science is provided in the following article “Scienti?c portrait of Alexander Vasil’evich Kazhikhov”. This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.
Collected Papers In Honor Of Yoshihiro Shibata
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Author : Tohru Ozawa
language : en
Publisher: Springer Nature
Release Date : 2022-11-30
Collected Papers In Honor Of Yoshihiro Shibata written by Tohru Ozawa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
Yoshihiro Shibata has made many significant contributions to the area of mathematical fluid mechanics over the course of his illustrious career, including landmark work on the Navier-Stokes equations. The papers collected here — on the occasion of his 70th birthday — are written by world-renowned researchers and celebrate his decades of outstanding achievements.
Nonlinear Partial Differential Equations
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Author : Helge Holden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-15
Nonlinear Partial Differential Equations written by Helge Holden 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 2012-01-15 with Mathematics categories.
The topic of the 2010 Abel Symposium, hosted at the Norwegian Academy of Science and Letters, Oslo, was Nonlinear Partial Differential Equations, the study of which is of fundamental importance in mathematics and in almost all of natural sciences, economics, and engineering. This area of mathematics is currently in the midst of an unprecedented development worldwide. Differential equations are used to model phenomena of increasing complexity, and in areas that have traditionally been outside the realm of mathematics. New analytical tools and numerical methods are dramatically improving our understanding of nonlinear models. Nonlinearity gives rise to novel effects reflected in the appearance of shock waves, turbulence, material defects, etc., and offers challenging mathematical problems. On the other hand, new mathematical developments provide new insight in many applications. These proceedings present a selection of the latest exciting results by world leading researchers.
Mathematical Theory Of Compressible Viscous Fluids
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Author : Eduard Feireisl
language : en
Publisher: Birkhäuser
Release Date : 2016-11-25
Mathematical Theory Of Compressible Viscous Fluids written by Eduard Feireisl and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-25 with Mathematics categories.
This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematics. It will help graduate students and researchers to not only better understand problems in mathematical compressible fluid mechanics but also to learn something from the field of mathematical and numerical analysis and to see the connections between the two worlds. Potential readers should possess a good command of the basic tools of functional analysis and partial differential equations including the function spaces of Sobolev type.
Nonlinear Conservation Laws And Applications
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Author : Alberto Bressan
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-19
Nonlinear Conservation Laws And Applications written by Alberto Bressan 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 2011-04-19 with Mathematics categories.
This volume contains the proceedings of the Summer Program on Nonlinear Conservation Laws and Applications held at the IMA on July 13--31, 2009. Hyperbolic conservation laws is a classical subject, which has experienced vigorous growth in recent years. The present collection provides a timely survey of the state of the art in this exciting field, and a comprehensive outlook on open problems. Contributions of more theoretical nature cover the following topics: global existence and uniqueness theory of one-dimensional systems, multidimensional conservation laws in several space variables and approximations of their solutions, mathematical analysis of fluid motion, stability and dynamics of viscous shock waves, singular limits for viscous systems, basic principles in the modeling of turbulent mixing, transonic flows past an obstacle and a fluid dynamic approach for isometric embedding in geometry, models of nonlinear elasticity, the Monge problem, and transport equations with rough coefficients. In addition, there are a number of papers devoted to applications. These include: models of blood flow, self-gravitating compressible fluids, granular flow, charge transport in fluids, and the modeling and control of traffic flow on networks.
Numerical Analysis Of Compressible Fluid Flows
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Author : Eduard Feireisl
language : en
Publisher: Springer Nature
Release Date : 2022-01-01
Numerical Analysis Of Compressible Fluid Flows written by Eduard Feireisl and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-01 with Mathematics categories.
This book is devoted to the numerical analysis of compressible fluids in the spirit of the celebrated Lax equivalence theorem. The text is aimed at graduate students in mathematics and fluid dynamics, researchers in applied mathematics, numerical analysis and scientific computing, and engineers and physicists. The book contains original theoretical material based on a new approach to generalized solutions (dissipative or measure-valued solutions). The concept of a weak-strong uniqueness principle in the class of generalized solutions is used to prove the convergence of various numerical methods. The problem of oscillatory solutions is solved by an original adaptation of the method of K-convergence. An effective method of computing the Young measures is presented. Theoretical results are illustrated by a series of numerical experiments. Applications of these concepts are to be expected in other problems of fluid mechanics and related fields.
Mathematics Of Open Fluid Systems
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Author : Eduard Feireisl
language : en
Publisher: Springer Nature
Release Date : 2022-04-01
Mathematics Of Open Fluid Systems written by Eduard Feireisl and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
The goal of this monograph is to develop a mathematical theory of open fluid systems in the framework of continuum thermodynamics. Part I discusses the difference between open and closed fluid systems and introduces the Navier-Stokes-Fourier system as the mathematical model of a fluid in motion that will be used throughout the text. A class of generalized solutions to the Navier-Stokes-Fourier system is considered in Part II in order to show existence of global-in-time solutions for any finite energy initial data, as well as to establish the weak-strong uniqueness principle. Finally, Part III addresses questions of asymptotic compactness and global boundedness of trajectories and briefly considers the statistical theory of turbulence and the validity of the ergodic hypothesis.