Mathematical Theory of Compressible Viscous Fluids Analysis and Numerics 1st Edition by Eduard Feireisl, Trygve Karper, Milan Pokorný 331944834X 9783319448343

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Product details:

ISBN 10: 331944834X

ISBN 13: 9783319448343

Author: Eduard Feireisl, Trygve G. Karper, Milan Pokorný

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.   

Table of contents:

1. Preliminaries, Notation, and Spaces of Functions

2. Mathematical Model

3. Weak Solutions

4. A Priori Bounds

5. Weak Formulation Revisited

6. Weak Sequential Stability

7. Numerical Method

8. Stability of the Numerical Method

9. Consistency

10. Convergence

11. Weak Solutions with Artificial Pressure

12. Strong Convergence of the Approximate Densities

13. Concluding Remarks and Suggestions for Further Reading

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Tags: Eduard Feireisl, Trygve Karper, Milan Pokorný, Compressible