Global well-posedness and decay estimates for three-dimensional compressible Navier-Stokes-Allen-Cahn system

Abstract

We study the small data global well-posedness and time-decay rates of solutions to the Cauchy problem for 3D compressible Navier-Stokes-Allen-Cahn equations via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained, the ${\dot{H}}^{-s}$ ($0\le s<\frac{3}{2}$) negative Sobolev norms is shown to be preserved along time evolution and enhance the decay rates.

28pages, 0 figure. arXiv admin note: text overlap with arXiv:1910.07904 and text overlap with arXiv:1112.4902 by other authors