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

Burtea, Cosmin; Haspot, Boris

Burtea, Cosmin; Haspot, Boris (2020), New effective pressure and existence of global strong solution for compressible Navier-Stokes equations with general viscosity coefficient in one dimension, Nonlinearity, 33, 5. 10.1088/1361-6544/ab7102

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Type

Article accepté pour publication ou publié

Date

2020

Journal name

Nonlinearity

Volume

Number

Publisher

IOP Science

Abstract (EN)

In this paper we prove the existence of global strong solution for the 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 technics developed by Hoff for the constant viscosity case.

Subjects / Keywords

PDe; Équation aux dérivées partielles; Navier-Stokes equations