Long time well-posedness of Prandtl system with small and analytic initial data
Long time well-posedness of Prandtl system with small and analytic initial data
复制标题
具有小量分析初始数据的 Prandtl 系统的长时间适定性
DOI：
10.1016/j.jfa.2016.01.004
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发表时间：
2016
影响因子：
1.7
通讯作者：
Zhang Zhifei
中科院分区：
文献类型：
--
作者：
Zhang Ping;Zhang Zhifei
本文研究了具有小初值的d= 2，3维Prandtl系统在水平变量下的小解的长时间存在性和唯一性.特别地，我们证明了当初始值为ε，流出切向速度边界值为ε 5 3时，d维Prandtl方程组存在唯一的解，其生存期大于ε− 4 3.文[4]、[5]中所发展的对该系统进行分析型估计的工具和非线性项的特殊结构在证明这一结果中起着重要作用。
In this paper, we investigate the long time existence and uniqueness of small solution to d, for d= 2, 3, dimensional Prandtl system with small initial data which is analytic in the horizontal variables. In particular, we prove that d dimensional Prandtl system has a unique solution with the life-span of which is greater than ε− 4 3 if the initial data is of size ε and the value on the boundary of the tangential velocity of the outflow are of size ε 5 3. We mention that the tool developed in [4],[5] to make the analytical type estimates and the special structure of the nonlinear terms to this system play an essential role in the proof of this result.