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

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 L-1(R-3), we derive the convergence rates of the kinetic energy and the potential energy to the Cauchy problem of the system with vacuum. (c) 2022 Published by Elsevier Ltd.