Overview
- Introduces the reader to the mathematical theory of compressible viscous fluids
- Provides the existence proof for the compressible Navier--Stokes system via a numerical scheme
- Presents analytical methods in view of numerical applications
Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)
Part of the book sub series: Lecture Notes in Mathematical Fluid Mechanics (LNMFM)
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About this book
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.
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Table of contents (13 chapters)
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Front Matter
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Mathematics of Compressible Fluid Flows
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Front Matter
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Existence of Weak Solutions via a Numerical Method
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Front Matter
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Existence Theory for General Pressure
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Front Matter
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Back Matter
Reviews
“The authors present the mathematical theory of compressible barotropic viscous fluids … . This very attractive, short and self-contained monograph is perfectly suitable for a beginning graduate student who wants to learn about mathematical fluid mechanics … .” (Bernard Ducomet, zbMATH 1356.76001, 2017)
Authors and Affiliations
About the authors
Eduard Feireisl is a Senior Researcher at the Institute of Mathematics of the Academy of Sciences of the Czech Republic. His main research interests include the theory of partial differential equations and dynamical systems with applications in fluid dynamics.
Milan Pokorny is an Associate Professor at the Charles University in Prague whose work primarily involves the theory of partial differential equations in mathematical fluid dynamics.
Trygve Karper is a researcher at Schlumberger whose work focuses on numerical methods for compressible flows and the multiphase flow simulator OLGA.
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Bibliographic Information
Book Title: Mathematical Theory of Compressible Viscous Fluids
Book Subtitle: Analysis and Numerics
Authors: Eduard Feireisl, Trygve G. Karper, Milan Pokorný
Series Title: Advances in Mathematical Fluid Mechanics
DOI: https://doi.org/10.1007/978-3-319-44835-0
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-44834-3Published: 30 November 2016
eBook ISBN: 978-3-319-44835-0Published: 25 November 2016
Series ISSN: 2297-0320
Series E-ISSN: 2297-0339
Edition Number: 1
Number of Pages: XII, 186
Number of Illustrations: 15 b/w illustrations
Topics: Partial Differential Equations, Numerical Analysis, Mathematical Methods in Physics, Fourier Analysis, Functional Analysis, Mathematical Applications in the Physical Sciences