Low Mach number limit of the compressible Navier–Stokes–Cattaneo equations with general initial data

Abstract

In this paper, we investigate the low Mach number limit of the compressible Navier–Stokes–Cattaneo equations in the whole space R3. In particular, the large variations of density, temperature and heat flux are taken into account. By introducing an appropriate time-weighted normed space, the uniform estimates of the solutions are established for general initial data. Then, the convergence of the solutions is proved by combining the uniform estimates and the local energy decay of acoustic waves. Finally, we derive a new limit equations which reveal the effect of heat flux on the field of velocity.