Vanishing pressure limit for compressible Navier–Stokes equations with degenerate viscosities

Abstract

In this paper we study a vanishing pressure process for highly compressible Navier–Stokes equations as the Mach number tends to infinity. We first prove the global existence of weak solutions for the pressureless system in the framework (Li and Xin 2015 arXiv:1504.06826v2), where the weak solutions are established for compressible Navier–Stokes equations with degenerate viscous coefficients. Furthermore, a rate of convergence of the density in is obtained, in case when the velocity corresponds to the gradient of density at initial time.