Optimal decay rates of isentropic compressible Navier-Stokes equations with discontinuous initial data

The global-in-time solutions with discontinuous initial data, when the density has no regularity, are constructed in [10–12] for the isentropic compressible Navier-Stokes equations in multi-dimensional spaces. The time decay rates of these solutions with low regularity still remain unsolved. In this paper we establish the decay rates of solutions in [10–12] in L^r-norm with 2≤r≤∞ and the decay rate of the first order derivative of the velocity in L²-norm when the initial data are bounded in L¹. The optimal decay rates are also obtained. These decay rates are the same as rates for classical solutions in [18,20].