A global existence result for a zero Mach number system
Analysis of PDEs
2014-03-14 v1
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.
Cite
@article{arxiv.1403.3154,
title = {A global existence result for a zero Mach number system},
author = {Xian Liao},
journal= {arXiv preprint arXiv:1403.3154},
year = {2014}
}