Navier-Stokes flow in the weighted Hardy space with applications to time decay problem
Navier-Stokes flow in the weighted Hardy space with applications to time decay problem
复制标题
加权 Hardy 空间中的纳维-斯托克斯流及其在时间衰减问题中的应用
DOI：
10.1016/j.jde.2016.04.014
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Takahiro Okabe and Yohei Tsutsui
中科院分区：
文献类型：
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作者：
Danielle Hilhorst;Mitsunori Nara;Takahiro Okabe and Yohei Tsutsui
借助于加权哈代空间，研究了Navier-Stokes流在Rn中的渐近展开及其衰减率. Fujigaki和Miyakawa [12]，Miyakawa [28]证明了当初始数据按（1+ 1）衰减时，Navier-Stokes流的n阶渐近展开式|X|）− n− 1，且初始数据的第n阶矩是有限的。在本文中，它是澄清的时刻条件的初始数据是必不可少的，以获得高阶渐近展开的流动，并考虑快速的时间衰减问题。第二作者[39]建立了Ln中具有小初值的加权哈代空间和一个加权哈代空间中强解的加权估计.首先，改进了以前的工作[39]，实现了替代证明。然后在没有任何哈代范数的情况下，刻画了该方程在加权哈代空间中解的存在时间.结果，在二维情况下，初始数据的小条件被完全去除。作为应用，借助于渐近展开式和Brandolese [3]引入的对称性条件，研究了流动的快速时间衰减。
The asymptotic expansions of the Navier–Stokes flow in R n and the rates of decay are studied with aid of weighted Hardy spaces. Fujigaki and Miyakawa [12], Miyakawa [28] proved the nth order asymptotic expansion of the Navier–Stokes flow if initial data decays like (1+| x|)− n− 1 and if nth moment of initial data is finite. In the present paper, it is clarified that the moment condition for initial data is essential in order to obtain higher order asymptotic expansion of the flow and to consider the rapid time decay problem. The second author [39] established the weighted estimates of the strong solutions in the weighted Hardy spaces with small initial data which belongs to L n and a weighed Hardy space. Firstly, the refinement of the previous work [39] is achieved with alternative proof. Then the existence time of the solution in the weighted Hardy spaces is characterized without any Hardy norm. As a result, in two dimensional case the smallness condition on initial data is completely removed. As an application, the rapid time decay of the flow is investigated with aid of asymptotic expansions and of the symmetry conditions introduced by Brandolese [3].