The low mach number limit of global solutions to the full compressible Navier-Stokes system in critical Besov spaces with large initial data

Abstract

We are concerned with global existence of regular solutions to full compressible Navier-Stokes equations and their asymptotic behavior when the Mach number is sufficiently small. We establish global existence in critical Besov spaces for arbitrary large initial date provided that the divergence-free component of initial velocity and the difference between initial temperature and density generate a global regular solution to incompressible Boussinesq systems. Moreover, we rigorously justify the convergence to the incompressible model as the Mach number tends to zero. The proof relies on a fine-grained analysis of the high-middle-low frequencies of density, velocity and temperature. Our result can be seen as an improvement on Danchin and He [Math. Ann., 366 (2016), no. 3-4, pp. 1365-1402], including the extension from small initial data to large initial data and new convergence results which hold at the level of critical regularity.