Asymptotic profiles for the compressible Navier–Stokes equations in the whole space

This paper is concerned with the large time behavior of strong solutions of the compressible Navier–Stokes equation in the whole space Rn(n≥3)Rn(n≥3) around the constant state. It was shown by Kawashima, Matsumura and Nishida (1979) and Hoff and Zumbrun (1995) that the perturbation of the constant state is time-asymptotic to a solution of the linearized problem, that is, a first-order asymptotic profile. In this paper a second-order asymptotic profile of the solution, which is caused by the nonlinear effect, is given.