A survey of the compressible Navier-Stokes equations

Benoît Desjardins; Chi Kun Lin

doi:10.11650/twjm/1500407089

A survey of the compressible Navier-Stokes equations

Benoît Desjardins^*, Chi Kun Lin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

21 Citations (Scopus)

Abstract

This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.

Original language	English
Pages (from-to)	123-137
Number of pages	15
Journal	Taiwanese Journal of Mathematics
Volume	3
Issue number	2
DOIs	https://doi.org/10.11650/twjm/1500407089
Publication status	Published - Jun 1999
Externally published	Yes

Keywords

Blow up
Compressibility
Entropy
Global weak solution
Incompressible limit
Regularity
Viscosity

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10.11650/twjm/1500407089

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title = "A survey of the compressible Navier-Stokes equations",

abstract = "This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.",

keywords = "Blow up, Compressibility, Entropy, Global weak solution, Incompressible limit, Regularity, Viscosity",

author = "Beno{\^i}t Desjardins and Lin, {Chi Kun}",

year = "1999",

month = jun,

doi = "10.11650/twjm/1500407089",

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AB - This paper presents mathematical properties of solutions to the Navier-Stokes equations for compressible fluids. We first review existence results for the Cauchy problem, and describe some regularity properties of solutions in the presence of possibly vanishing densities. Finally, we address the problem of the low Mach number limit leading to incompressible models.

KW - Blow up

KW - Compressibility

KW - Entropy

KW - Global weak solution

KW - Incompressible limit

KW - Regularity

KW - Viscosity

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DO - 10.11650/twjm/1500407089

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A survey of the compressible Navier-Stokes equations

Abstract

Keywords

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