Local-in-Time Existence and Uniqueness of Solutions to the Prandtl Equations by Energy Methods

被引：166

作者：

Masmoudi, Nader ^{[1
]}

Wong, Tak Kwong ^{[2
]}

机构：

[1] NYU, Courant Inst, New York, NY 10012 USA

[2] Univ Penn, Dept Math, David Rittenhouse Lab, Philadelphia, PA 19104 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2015年 / 68卷 / 10期

基金：

美国国家科学基金会;

关键词：

NAVIER-STOKES EQUATIONS; ZERO VISCOSITY LIMIT; BOUNDARY-LAYER; ANALYTIC SOLUTIONS; VANISHING VISCOSITY; INVISCID LIMIT; WELL-POSEDNESS; ILL-POSEDNESS; HALF-SPACE; EULER;

D O I：

10.1002/cpa.21595

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove local existence and uniqueness for the two-dimensional Prandtl system in weighted Sobolev spaces under Oleinik's monotonicity assumption. In particular we do not use the Crocco transform or any change of variables. Our proof is based on a new nonlinear energy estimate for the Prandtl system. This new energy estimate is based on a cancellation property that is valid under the monotonicity assumption. To construct the solution, we use a regularization of the system that preserves this nonlinear structure. This new nonlinear structure may give some insight into the convergence properties from the Navier-Stokes system to the Euler system when the viscosity goes to 0. (c) 2015 Wiley Periodicals, Inc.

引用

页码：1683 / 1741

页数：59

共 42 条

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