A global existence result for a zero Mach number system

Abstract

This paper is to study global-in-time existence of weak solutions to zero Mach number system which derives from the full Navier-Stokes system, under a special relationship between the viscosity coefficient and the heat conductivity coefficient such that, roughly speaking, 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 in \cite{Danchin-Liao}, for arbitrary large initial data, we will show that this unique strong solution exists globally in time, by a weak-strong uniqueness argument.

References in corpus (1)

• Low Mach number limit of the full Navier-Stokes equations

Cited by in corpus (3)

• The well-posedness issue for an inviscid zero-Mach number system in general Besov spaces
• Analysis of an inviscid zero-Mach number system in endpoint Besov spaces with finite-energy initial data
• On the two-dimensional Boussinesq equations with temperature-dependent thermal and viscosity diffusions in general Sobolev spaces