Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations
Global existence and time-decay estimates of solutions to the compressible Navier-Stokes-Smoluchowski equations
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DOI：
10.3934/dcds.2016032
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发表时间：
2016-07
影响因子：
1.1
通讯作者：
Yingshan Chen;S. Ding;Wenjun Wang
中科院分区：
文献类型：
--
作者：
Yingshan Chen;S. Ding;Wenjun Wang
This paper is concerned with the Cauchy problem of the compressible Navier-Stokes-Smoluchowski equations in $\mathbb{R}^3$. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence theory of global solutions in $H^3$ to the stationary profile is established. Moreover, when the initial perturbation is bounded in $L^p$-norm with $1\leq p< \frac{6}{5}$, we obtain the optimal convergence rates of the solution in $L^q$-norm with $2\leq q\leq 6$ and its first order derivative in $L^2$-norm.
