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Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids Read chapter Read first chapter

2018 | OriginalPaper | Chapter

32. Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class

Author : Misha Perepelitsa

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

Publisher: Springer International Publishing

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Abstract

In this chapter we discuss an initial-boundary value problem for the Navier-Stokes equations for compressible flows in bounded domains with the no-slip boundary conditions for the velocity. We demonstrate the existence of weak solutions that belong to the intermediate regularity class, with strictly positive and uniformly bounded density and Hölder continuous velocity. The result is proved under the assumption that the initial data are close to a static equilibrium.

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previous chapter Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases
next chapter Symmetric Solutions to the Viscous Gas Equations
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Metadata
Title
Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class
Author
Misha Perepelitsa
Copyright Year
2018
Book
Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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

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

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-13344-7_45

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