an:05881778
Zbl 1214.35047
Li, Hai-Liang; Zhang, Ting
Large time behavior of isentropic compressible Navier-Stokes system in \(\mathbb R^3\)
EN
Math. Methods Appl. Sci. 34, No. 6, 670-682 (2011).
00277133
2011
j
35Q30 76N10 35B40 35B30
compressible Navier-Stokes system; optimal decay rate
Summary: 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 \(H^l(\mathbb R^3)\cap\dot B_{1,\infty}^{-s}(\mathbb R^3)\) with \(l\geq 4\) and \(s\in [0,1]\), 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 \(L^\infty\)-norm, respectively, which are shown to be optimal for the CNS system.