On stability of weak Navier-Stokes solutions with large L3,∞ initial data.
On stability of weak Navier-Stokes solutions with large L3,∞ initial data.
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关于具有大 L3 的弱 Navier-Stokes 解的稳定性，初始数据。
DOI：
10.1080/03605302.2018.1449219
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发表时间：
2018
影响因子：
1.9
通讯作者：
Sverak, Vladimir
中科院分区：
文献类型：
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作者：
Barker, Tobias;Seregin, Gregory;Sverak, Vladimir
我们考虑了ℝ3×0，∞[中的N-S方程的柯西问题，初始数据是包含非平凡的(−1)−齐次场的临界空间。利用微扰理论，Smallone可以得到全局适定性。当它不小时，微扰理论不再适用，并且很可能是局部时间适定性和唯一性失效。人们仍然可以发展出一个具有如下稳定性的弱解理论：如果u(N)是对应于初始数据的弱解，并且弱收敛到0，则FU(N)的适当的子序列收敛到对应于初始条件u0的弱解。即使在特殊情况下，这一点也很有意义：0≡0。
We consider the Cauchy problem for the Navier–Stokes equation in ℝ3×]0,∞[ with the initial datum, a critical space containing nontrivial (−1)−homogeneous fields. For smallone can get global well-posedness by perturbation theory. Whenis not small, the perturbation theory no longer applies and, very likely, the local-in-time well-posedness and uniqueness fails. One can still develop a good theory of weak solutions with the following stability property: Ifu(n)are weak solutions corresponding the the initial datum, andconverge weakly* intou0, then a suitable subsequence ofu(n)converges to a weak solutionucorresponding to the initial conditionu0. This is of interest even in the special caseu0≡0.