A Global Existence Result for a Zero Mach Number System

作者：Liao Xian^*

来源：Journal of Mathematical Fluid Mechanics, 2014, 16(1): 77-103.

DOI：10.1007/s00021-013-0152-3

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

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.

• 出版日期2014-3