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Mathematical Theory of Compressible Viscous Fluids

Analysis and Numerics

  • Eduard Feireisl
  • Trygve G. Karper
  • Milan Pokorný

Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Also part of the Lecture Notes in Mathematical Fluid Mechanics book sub series (LNMFM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
    Pages 1-22
  3. Mathematics of Compressible Fluid Flows

    1. Front Matter
      Pages 23-23
    2. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 25-30
    3. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 31-38
    4. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 39-47
    5. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 49-53
    6. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 55-77
  4. Existence of Weak Solutions via a Numerical Method

    1. Front Matter
      Pages 79-79
    2. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 81-102
    3. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 103-109
    4. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 111-133
    5. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 135-154
  5. Existence Theory for General Pressure

    1. Front Matter
      Pages 155-155
    2. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 157-164
    3. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 165-176
    4. Eduard Feireisl, Trygve G. Karper, Milan Pokorný
      Pages 177-178
  6. Back Matter
    Pages 179-186

About this book

Introduction

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.

 

Keywords

compressible Navier-Stokes system weak solution well-posedness upwind discretization discontinuous Galerkin method compressible viscous fluids

Authors and affiliations

  • Eduard Feireisl
    • 1
  • Trygve G. Karper
    • 2
  • Milan Pokorný
    • 3
  1. 1.Institute of Mathematics CASPrahaCzech Republic
  2. 2.Department of Mathematical SciencesNorwegian University of Science & Tech.TrondheimNorway
  3. 3.Charles UniversityFaculty Mathematics and Physics Charles UniversityPrahaCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-44835-0
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-44834-3
  • Online ISBN 978-3-319-44835-0
  • Series Print ISSN 2297-0320
  • Series Online ISSN 2297-0339
  • Buy this book on publisher's site