Large time behavior of isentropic compressible Navier–Stokes system in ℝ3
Large time behavior of isentropic compressible Navier–Stokes system in ℝ3
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DOI：
10.1002/mma.1391
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发表时间：
2011-04
影响因子：
2.9
通讯作者：
Hai-liang Li;Ting Zhang
中科院分区：
文献类型：
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作者：
Hai-liang Li;Ting Zhang
本文研究了三维等熵可压缩Navier-Stokes （CNS）系统全局强解的长时间行为和最优衰减率。当规则初始数据也属于l大于或等于4且s∈[0,1]的某些Sobolev空间时，我们表明CNS系统的全局解在时间上以更快的衰减率收敛到平衡状态。特别是，密度和动量分别以L2范数(1 + t)−3/4−s/2和L∞范数(1 + t)−3/2−s/2的速率收敛到平衡态，这对CNS系统来说是最优的。版权所有©2010 John Wiley & Sons， Ltd
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.