Well-posedness of the linearized Prandtl equation around a non-monotonic shear flow

被引:32
作者
Chen, Dongxiang [1 ]
Wang, Yuxi [2 ]
Zhang, Zhifei [2 ]
机构
[1] Jiangxi Normal Univ, Coll Math & Informat Sci, Nanchang 330022, Jiangxi, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2018年 / 35卷 / 04期
关键词
Prandtl equation; Gevrey class; Well-posedness; ILL-POSEDNESS; EXISTENCE; SYSTEM; MONOTONICITY; EULER;
D O I
10.1016/j.anihpc.2017.11.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we prove the well-posedness of the linearized Prandtl equation around a non-monotonic shear flow in Gevrey class 2 - theta for any theta > 0. This result is almost optimal by the ill-posedness result proved by Gerard-Varet and Dormy, who construct a class of solution with the growth like e root(kt) for the linearized Prandtl equation around a non-monotonic shear flow. (C) 2017 Elsevier Masson SAS. All rights reserved.
引用
收藏
页码:1119 / 1142
页数:24
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