New effective pressure and existence of global strong solution for compressible Navier-Stokes equations with general viscosity coefficient in one dimension

被引：14

作者：

Burtea, Cosmin ^{[1
]}

Haspot, Boris ^{[2
,3
]}

机构：

[1] Univ Paris Diderot, Sorbonne Paris Cite, UMR 7586, Inst Math Jussieu Paris Rive Gauche, F-75205 Paris, France

[2] PSL Res Univ, Univ Paris Dauphine, CEREMADE, Umr Cnrs 7534, Pl Marechal De Lattre De Tassigny 75775, F-75775 Paris 16, France

[3] CNRS, UPMC, Cerema, ANGE Project Team,Inria, 2 Rue Simone Iff,CS 42112, F-75589 Paris, France

来源：

NONLINEARITY | 2020年 / 33卷 / 05期

关键词：

Navier-Stokes equations; fluid mechanics; effective pressure; WEAK SOLUTIONS; 1D;

D O I：

10.1088/1361-6544/ab7102

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the existence of a unique global strong solution for the Cauchy problem associated to the one dimensional Navier-Stokes equations with general degenerate viscosity coefficients. The cornerstone of the proof is the introduction of a new effective pressure which allows to obtain an Oleinik-type estimate for the so called effective velocity. In our proof we make use of additional regularizing effects on the velocity which requires to extend the techniques developed by Hoff for the constant viscosity case.

引用

页码：2077 / 2105

页数：29

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