Lower bound of $L^2$ decay of the Navier-Stokes flow in the half-space $R_+^n$ and its asymptotic behavior in the frequency space
Lower bound of $L^2$ decay of the Navier-Stokes flow in the half-space $R_+^n$ and its asymptotic behavior in the frequency space
复制标题
半空间 $R_ ^n$ 中纳维-斯托克斯流的 $L^2$ 衰减下界及其在频率空间中的渐近行为
DOI：
10.1016/j.jmaa.2012.12.033
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Takahiro Okabe
中科院分区：
文献类型：
--
作者：
Satomi Murakami;Hiroki Ohwa;應和 宏樹;Takahiro Okabe
研究半空间R+n中Navier-Stokes方程弱解的渐近性态。利用初始数据的轮廓，我们得到了Navier-Stokes流能量衰减的下界。事实上，我们构造了一类初始数据，导致Navier-Stokes流的缓慢衰减，具有明确的速率。此外，我们还研究了浓度在频率空间中的渐近行为。
We consider the asymptotic behavior of weak solutions of the Navier–Stokes equations in the half-space R+n. We obtain the lower bound of the energy decay of the Navier–Stokes flow, by means of the profile of the initial data. Indeed, we construct a class of the initial data which causes the slow decay of the Navier–Stokes flow, with an explicit rate. Furthermore, we investigate the asymptotic behavior of concentration in the frequency space.