Mathematical Theory of Compressible Viscous Fluids

Analysis and Numerics

Authors:

ISBN: 978-3-319-44834-3 (Print) 978-3-319-44835-0 (Online)

Table of contents (13 chapters)

  1. Front Matter

    Pages i-xii

  2. No Access

    Chapter

    Pages 1-22

    Preliminaries, Notation, and Spaces of Functions

  3. Mathematics of Compressible Fluid Flows

    1. Front Matter

      Pages 23-23

    2. No Access

      Chapter

      Pages 25-30

      Mathematical Model

    3. No Access

      Chapter

      Pages 31-38

      Weak Solutions

    4. No Access

      Chapter

      Pages 39-47

      A Priori Bounds

    5. No Access

      Chapter

      Pages 49-53

      Weak Formulation Revisited

    6. No Access

      Chapter

      Pages 55-77

      Weak Sequential Stability

  4. Existence of Weak Solutions via a Numerical Method

    1. Front Matter

      Pages 79-79

    2. No Access

      Chapter

      Pages 81-102

      Numerical Method

    3. No Access

      Chapter

      Pages 103-109

      Stability of the Numerical Method

    4. No Access

      Chapter

      Pages 111-133

      Consistency

    5. No Access

      Chapter

      Pages 135-154

      Convergence

  5. Existence Theory for General Pressure

    1. Front Matter

      Pages 155-155

    2. No Access

      Chapter

      Pages 157-164

      Weak Solutions with Artificial Pressure

    3. No Access

      Chapter

      Pages 165-176

      Strong Convergence of the Approximate Densities

    4. No Access

      Chapter

      Pages 177-178

      Concluding Remarks and Suggestions for Further Reading

  6. Back Matter

    Pages 179-186