Large time behavior of isentropic compressible Navier-Stokes system in <i>ℝ</i> ³

Abstract

We consider the long-time behavior and optimal decay rates of global strong solution to three-dimensional isentropic compressible Navier–Stokes (CNS) system in the present paper. When the regular initial data also belong to some Sobolev space with l⩾4 and s∈[0, 1], we show that the global solution to the CNS system converges to the equilibrium state at a faster decay rate in time. In particular, the density and momentum converge to the equilibrium state at the rates (1 + t)−3/4−s/2 in the L2-norm or (1 + t)−3/2−s/2 in the L∞-norm, respectively, which are shown to be optimal for the CNS system. Copyright © 2010 John Wiley & Sons, Ltd.