Optimal decay rate for strong solutions in critical spaces to the compressible Navier-Stokes equations

In this paper we are concerned with the convergence rates of the global strong solution to motionless state with constant density for the compressible Navier-Stokes equations in the whole space Rn for n≥3. It is proved that the perturbations decay in critical spaces, if the initial perturbations of density and velocity are small in B2,1n2(Rn)∩B˙1,∞0(Rn) and B2,1n2−1(Rn)∩B˙1,∞0(Rn), respectively.