Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow
Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow
复制标题
DOI：
10.1016/j.anihpc.2017.11.001
复制
发表时间：
2016-09
期刊：
影响因子：
--
通讯作者：
Dongxiang Chen;Yuxi Wang;Zhifei Zhang
中科院分区：
文献类型：
--
作者：
Dongxiang Chen;Yuxi Wang;Zhifei Zhang
本文证明了线性化Prandtl方程在Gevrey类2-θ中的非单调剪切流中的适定性，其中θ> 0.这一结果与Gérard-Varet和Dormy关于线性化Prandtl方程在非单调剪切流中构造了一类增长型解的不适定性结果相比几乎是最优的。
In this paper, we prove the well-posedness of the linearized Prandtl equation around a non-monotonic shear flow in Gevrey class 2− θ for any θ> 0. This result is almost optimal by the ill-posedness result proved by Gérard-Varet and Dormy, who construct a class of solution with the growth like e k t for the linearized Prandtl equation around a non-monotonic shear flow.