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Erschienen in:
Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

29. Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior

verfasst von : Antonín Novotný, Hana Petzeltová

Erschienen in: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Verlag: Springer International Publishing

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Abstract

This double-sized chapter contains two related themes that were supposed to be covered by two independent chapters of the handbook in the original project:

  1. (1)

    weak solutions of the Navier-Stokes equations in the barotropic regime and

     
  2. (2)

    weak solutions of the Navier-Stokes-Fourier system.

     
We shall discuss for both systems:
  1. (1)

    Various notions of weak solutions, their relevance, and their mutual relations.

     
  2. (2)

    Global existence of weak solutions.

     
  3. (3)

    Notions of relative energy functional, dissipative solutions and relative energy inequality and its impact on the investigation of the stability analysis of compressible flows.

     
  4. (4)

    Weak strong uniqueness principle.

     
  5. (5)

    Longtime behavior of weak solutions.

     

For physical reasons, we shall limit ourselves to the three-dimensional physical space.

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Vorheriges Kapitel Concepts of Solutions in the Thermodynamics of Compressible Fluids
Nächstes Kapitel Weak Solutions for the Compressible Navier-Stokes Equations with Density Dependent Viscosities
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Metadaten
Titel
Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior
verfasst von
Antonín Novotný
Hana Petzeltová
Copyright-Jahr
2018
Buch
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Print ISBN: 978-3-319-13343-0

Electronic ISBN: 978-3-319-13344-7

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-13344-7_76