Mathematical Theory Of Compressible Viscous Fluids
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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.
Dynamics Of Viscous Compressible Fluids
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Author : Eduard Feireisl
language : en
Publisher: Oxford University Press
Release Date : 2004
Dynamics Of Viscous Compressible Fluids written by Eduard Feireisl and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Language Arts & Disciplines categories.
This text develops the ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research.
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.
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)
Introduction To The Mathematical Theory Of Compressible Flow
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Author : Antonín Novotny
language : en
Publisher: OUP Oxford
Release Date : 2004-06-17
Introduction To The Mathematical Theory Of Compressible Flow written by Antonín Novotny and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-17 with Mathematics categories.
This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.
Theory And Applications Of Viscous Fluid Flows
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Author : Radyadour Kh. Zeytounian
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-08-25
Theory And Applications Of Viscous Fluid Flows written by Radyadour Kh. Zeytounian 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 2003-08-25 with Science categories.
This book closes the gap between standard undergraduate texts on fluid mechanics and monographical publications devoted to specific aspects of viscous fluid flows. Each chapter serves as an introduction to a special topic that will facilitate later application by readers in their research work.
Mathematical Theory Of Compressible Fluids On Moving Domains
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Author : Ondřej Kreml
language : en
Publisher: Springer Nature
Release Date : 2025-02-27
Mathematical Theory Of Compressible Fluids On Moving Domains written by Ondřej Kreml and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Mathematics categories.
This monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed. Chapters build upon the research of Lions and Feireisl with regards to weak solutions to the compressible version of the Navier-Stokes system, and extend it to problems on moving domains. The authors also show the existence of strong solutions to the compressible Navier-Stokes system for either a small time interval or small data. The opening chapters introduce the notation, tools, and problems covered in the rest of the book, emphasizing pedagogy and accessibility throughout. Mathematical Theory of Compressible Fluids on Moving Domains will be suitable for graduate students and researchers interested in mathematical fluid mechanics.
Navier Stokes Equations In Planar Domains
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Author : Matania Ben-artzi
language : en
Publisher: World Scientific
Release Date : 2013-03-07
Navier Stokes Equations In Planar Domains written by Matania Ben-artzi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Mathematics categories.
This volume deals with the classical Navier-Stokes system of equations governing the planar flow of incompressible, viscid fluid. It is a first-of-its-kind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as “driven cavity” and “double-driven cavity”.A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a “pure streamfunction” approach. In particular, a complete proof of convergence is given for the full nonlinear problem.This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics./a
Theory And Applications Of Viscous Fluid Flows
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Author : Radyadour Kh. Zeytounian
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Theory And Applications Of Viscous Fluid Flows written by Radyadour Kh. Zeytounian 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 2013-06-29 with Science categories.
This book is the natural sequel to the study of nonviscous fluid flows pre sented in our recent book entitled "Theory and Applications of Nonviscous Fluid Flows" and published in 2002 by the Physics Editorial Department of Springer-Verlag (ISBN 3-540-41412-6 Springer-Verlag, Berlin, Heidelberg, New York). The physical concept of viscosity (for so-called "real fluids") is associated both incompressible and compressible fluids. Consequently, we have with a vast field of theoretical study and applications from which any subsection could have itself provided an area for a single book. It was, however, decided to attempt aglobaI study so that each chapter serves as an introduction to more specialized study, and the book as a whole presents a necessary broad foundation for furt her study in depth. Consequently, this volume contains many more pages than my preceding book devoted to nonviscous fluid flows and a large number (80) of figures. There are three main models for the study of viscous fluid flows: First, the model linked with viscous incompressible fluid flows, the so-called (dynamic) Navier model, governing linearly viscous divergenceless and homogeneous fluid flows. The second is the sü-called Navier-Stokes model (NS) which is linked to compressible, linearly viscous and isentropic equations für a polytropic viscous gas. The third is the so-called Navier-Stokes-Fourier model (NSF) that gov erns the motion of a compressible, linearly viscous, heat-conducting gas.
Recent Topics On Mathematical Theory Of Viscous Incompressible Fluid
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Author : Hideo Kozono
language : en
Publisher:
Release Date : 1998
Recent Topics On Mathematical Theory Of Viscous Incompressible Fluid written by Hideo Kozono and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Fluid dynamics categories.