Zero-Mach limit of the compressible Navier-Stokes system on 2D exterior domains with non-slip boundary conditions for all time

Abstract

We prove the zero-Mach limit of the compressible Navier-Stokes system on 2D exterior domains with non-slip boundary conditions for all time. Compared with the previous works on the domain with no boundary or slip boundary conditions, the non-slip conditions generate essential difficulties in obtaining uniform near-boundary estimates of smooth solutions. The key ingredient of our work includes the derivation of uniform estimates for the high order derivatives of the density from the hyperbolic dissipations. Moreover, we develop some new global geometric tools based on the decomposition of Euclidean metric to handle the tough boundary estimates, and the method seems applicable for other boundary problems on exterior domains as well.