ON THE CONVERGENCE RATES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH POTENTIAL FORCE

In this paper we are concerned with the optimal convergence rates of the global strong solution to the stationary solutions for the compressible Navier-Stokes equations with a potential external force ∇Φ in the whole space R^n for n ≥ 3. It is proved that the perturbation and its first-order derivatives decay in L ^ 2 norm in O(t^<-n/4> ) and O(t^<-n/4-1/2>), respectively, which are of the same order as those of the n-dimensional heat kernel, if the initial perturbation is small in H^<s_0>(R^n) ∩ L^1(R^n) with s_0 =[n/2]+ 1 and the potential force Φ is small in some Sobolev space. The results also hold for n ≥ 2 when Φ = 0. When Φ = 0, we also obtain the decay rates of higher-order derivatives of perturbations