Large time behavior of isentropic compressible Navier-Stokes system in ?~3

摘要

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 H(?~3) ∩ B_(1,α)~(-s) (?~3) with 1 ≥ 4 and s e[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 L ~2-norm or (1 + t)~(-3/2-s/2) in the L~2-norm, respectively, which are shown to be optimal for the CNS system.