Optimal L^p - L^q convergence rates for the compressible Navier-Stokes equations with potential force

In this paper, we are concerned with the optimal L^p - L^q convergence rates for the compressible Navier-Stokes equations with a potential external force in the whole space. Under the smallness assumption on both the initial perturbation and the external force in some Sobolev spaces, the optimal convergence rates of the solution in L^q-norm with 2 ≤ q ≤ 6 and its first order derivative in L²-norm are obtained when the initial perturbation is bounded in L^p with 1 ≤ p <6 / 5. The proof is based on the energy estimates on the solution to the nonlinear problem and some L^p - L^q estimates on the semigroup generated by the corresponding linearized operator. © 2007 Elsevier Inc. All rights reserved.