Large-time behavior of the energy to the isentropic compressible Navier–Stokes equations with vacuum

Abstract

In the present paper, we study the large-time behavior of the energy to the isentropic compressible Navier–Stokes equations in R3. More exactly, under the assumption that the initial data are of small energy but possibly large oscillations, and in addition that the initial density belongs to L1(R3), we derive the convergence rates of the kinetic energy and the potential energy to the Cauchy problem of the system with vacuum.