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Journal of Mathematical Fluid Mechanics

, Volume 16, Issue 1, pp 77–103 | Cite as

A Global Existence Result for a Zero Mach Number System

  • Xian LiaoEmail author
Article

Abstract

In this paper we study the global-in-time existence of weak solutions to a zero Mach number system that derives from the Navier–Stokes–Fourier system, under a special relationship between the viscosity coefficient and the heat conductivity coefficient. Roughly speaking, this relation implies that the source term in the equation for the newly introduced divergence-free velocity vector field vanishes. In dimension two, thanks to a local-in-time existence result of a unique strong solution in critical Besov spaces given by Danchin and Liao (Commun Contemp Math 14:1250022, 2012), for arbitrary large initial data, we show that this unique strong solution exists globally in time, as a consequence of a weak-strong uniqueness argument.

Mathematics Subject Classification (2010)

Primary 35Q30 Secondary 76R50 

Keywords

Zero Mach number system Cauchy problem weak solutions global-in-time existence weak-strong uniqueness Besov spaces 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Université Paris-Est Créteil, LAMACréteilFrance

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