Well-posedness of the Prandtl equation with monotonicity in Sobolev spaces

被引：12

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：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 09期

基金：

美国国家科学基金会;

关键词：

ZERO-VISCOSITY LIMIT; ILL-POSEDNESS; EXISTENCE; EULER;

D O I：

10.1016/j.jde.2018.01.0240022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By using the paralinearization technique, we prove the well-posedness of the Prandtl equation for monotonic data in anisotropic Sobolev space with exponential weight and low regularity. The proof is very elementary, thus is expected to provide a new possible way for the zero-viscosity limit problem of the Navier-Stokes equations with the non-slip boundary condition. (c) 2018 Elsevier Inc. All rights reserved.

引用

页码：5870 / 5893

页数：24

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