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

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NScompressible_ready_for_submission.pdf (413.6Kb)
Date
2020
Dewey
Probabilités et mathématiques appliquées
Sujet
PDe; Équation aux dérivées partielles; Navier-Stokes equations
Journal issue
Nonlinearity
Volume
33
Number
5
Publication date
2020
Publisher
IOP Science
DOI
http://dx.doi.org/10.1088/1361-6544/ab7102
URI
https://basepub.dauphine.fr/handle/123456789/20649
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  • CEREMADE : Publications
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Author
Burtea, Cosmin
Haspot, Boris
Type
Article accepté pour publication ou publié
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.

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