Decay of the non-isentropic Navier-Stokes-Poisson equations
Decay of the non-isentropic Navier-Stokes-Poisson equations
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DOI：
10.1016/j.jmaa.2012.09.021
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发表时间：
2013-04
影响因子：
1.3
通讯作者：
Zhong Tan;Xu Zhang
中科院分区：
文献类型：
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作者：
Zhong Tan;Xu Zhang
利用一种改进的纯能量方法，建立了非等熵可压缩Navier-Stokes-Poisson系统Cauchy问题解的时间衰减率。特别地，得到了解的高阶空间导数的最优衰减率。作为推论，我们也得到了通常的Lp−L2（1<p≤2）型的最优衰减率。随着时间的推移，Ḣ−s（0≤s<3/2）负索博列夫范数保持不变，并提高了衰变速率。我们使用一组具有最小导数计数和插值的缩放能量估计，而不需要线性衰减分析。
We establish the time decay rates of the solution to the Cauchy problem for the non-isentropic compressible Navier–Stokes–Poisson system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of the solution are obtained. As a corollary, we also obtain the usual Lp−L2(1<p≤2) type of the optimal decay rates. The Ḣ−s(0≤s<3/2) negative Sobolev norms are shown to be preserved along time evolution and enhance the decay rates. We use a family of scaled energy estimates with minimum derivative counts and interpolations among them without linear decay analysis.