Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids
Haspot, Boris (2011), Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids, Archive for Rational Mechanics and Analysis, 202, 2, p. 427-460. http://dx.doi.org/10.1007/s00205-011-0430-2
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Article accepté pour publication ou publiéLien vers un document non conservé dans cette base
http://arxiv.org/abs/1005.0706v1Date
2011Nom de la revue
Archive for Rational Mechanics and AnalysisVolume
202Numéro
2Éditeur
Springer
Pages
427-460
Identifiant publication
Métadonnées
Afficher la notice complèteAuteur(s)
Haspot, BorisRésumé (EN)
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≧ 2. We address the question of the global existence of strong solutions for initial data close to a constant state having critical Besov regularity. First, this article shows the recent results of Charve and Danchin (Arch Ration Mech Anal 198(1):233–271, 2010) and Chen et al. (Commun Pure Appl Math 63:1173–1224, 2010) with a new proof. Our result relies on a new a priori estimate for the velocity that we derive via the intermediary of the effective velocity, which allows us to cancel out the coupling between the density and the velocity as in Haspot (Well-posedness in critical spaces for barotropic viscous fluids, 2009). Second, we improve the results of Charve and Danchin (2010) and Chen et al. (2010) by adding as in Charve and Danchin (2010) some regularity on the initial data in low frequencies. In this case we obtain global strong solutions for a class of large initial data which rely on the results of Hoff (Arch Rational Mech Anal 139:303–354, 1997), Hoff (Commun Pure Appl Math 55(11):1365–1407, 2002), and Hoff (J Math Fluid Mech 7(3):315–338, 2005) and those of Charve and Danchin (2010) and Chen et al. (2010). We conclude by generalizing these results for general viscosity coefficients.Mots-clés
barotropic viscous fluidsPublications associées
Affichage des éléments liés par titre et auteur.
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