A blow-up criterion of strong solution to a 3D viscous liquid–gas two-phase flow model with vacuum

In this paper, we get a unique local strong solution to a 3D viscous liquid–gas two-phase flow model in a smooth bounded domain. Besides, a blow-up criterion of the strong solution for 253μ>λ is obtained. The method can be applied to study a blow-up criterion of the strong solution to Navier–Stok...

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Bibliographic Details
Published in:Journal de mathématiques pures et appliquées 2012-03, Vol.97 (3), p.204-229
Main Authors: Wen, Huanyao, Yao, Lei, Zhu, Changjiang
Format: Article
Language:English
Subjects:
Blow-up criterion
Exact sciences and technology
General mathematics
General, history and biography
Liquid–gas two-phase flow model
Local strong solution
Mathematical analysis
Mathematics
Partial differential equations
Sciences and techniques of general use
Vacuum
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Summary:In this paper, we get a unique local strong solution to a 3D viscous liquid–gas two-phase flow model in a smooth bounded domain. Besides, a blow-up criterion of the strong solution for 253μ>λ is obtained. The method can be applied to study a blow-up criterion of the strong solution to Navier–Stokes equations for 253μ>λ, which improves the corresponding result about Navier–Stokes equations in Sun et al. (2011) [15] where 7μ>λ. Moreover, all the results permit the appearance of vacuum. Dans cet article, on démontre lʼexistence dʼune solution classique tridimensionelle pour un modèle dʼécoulement visqueux diphasique (liquide–gaz) dans un domaine borné et régulier. De plus, on établit un critère dʼexplosion de la solution lorsque 253μ>λ. La même méthode sʼapplique pour établir lʼexplosion de solution classique des équations de Navier–Stokes lorsque 253μ>λ, ce qui améliore le résultat correspondant obtenu dans Sun et al. (2011) [15] où lʼexplosion est établie pour 7μ>λ. Enfin, tous les résultats restent valables en présence de vide.
ISSN:0021-7824
DOI:10.1016/j.matpur.2011.09.005