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

页码：1119 / 1142

页数：24

共 15 条

[1]

Alexandre R, 2015, J AM MATH SOC, V28, P745

[2]

Chen D., WELL POSEDNESS UNPUB

[3] Remarks on the ill-posedness of the Prandtl equation [J].

Gerard-Varet, D. ;

Nguyen, T. .

ASYMPTOTIC ANALYSIS, 2012, 77 (1-2) :71-88

[4]

Gérard-Varet D, 2015, ANN SCI ECOLE NORM S, V48, P1273

[5]

Gérard-Varet D, 2010, J AM MATH SOC, V23, P591

[6] A Note on Prandtl Boundary Layers [J].

Guo, Yan ;

Toan Nguyen .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (10) :1416-1438

[7] ON THE LOCAL WELL-POSEDNESS OF THE PRANDTL AND HYDROSTATIC EULER EQUATIONS WITH MULTIPLE MONOTONICITY REGIONS [J].

Kukavica, Igor ;

Masmoudi, Nader ;

Vicol, Vlad ;

Wong, Tak Kwong .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2014, 46 (06) :3865-3890

[8]

Li W., ARXIV160908430

[9] Well-posedness of the boundary layer equations [J].

Lombardo, MC ;

Cannone, M ;

Sammartino, M .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (04) :987-1004

[10] Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods [J].

Masmoudi, Nader ;

Wong, Tak Kwong .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2015, 68 (10) :1683-1741

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