Well-Posedness in Gevrey Function Space for 3D Prandtl Equations without Structural Assumption

被引：20

作者：

Li, Wei-Xi ^{[1
,2
]}

Masmoudi, Nader ^{[3
,4
]}

Yang, Tong ^{[5
]}

机构：

[1] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Peoples R China

[2] Wuhan Univ, Hubei Key Lab Computat Sci, Wuhan 430072, Peoples R China

[3] Courant Inst, 251 Mercer St, New York, NY 10012 USA

[4] NYU Abu Dhabi, Abu Dhabi, U Arab Emirates

[5] City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2022年 / 75卷 / 08期

关键词：

ILL-POSEDNESS; INVISCID LIMIT; INSTABILITY; EXPANSIONS; EXISTENCE; STABILITY; EULER; FLOWS;

D O I：

10.1002/cpa.21989

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the well-posedness in Gevrey function space with optimal class of regularity 2 for the three-dimensional Prandtl system without any structural assumption. The proof combines in a novel way a new cancellation in the system with some of the old ideas to overcome the difficulty of the loss of derivatives in the system. This shows that the three-dimensional instabilities in the system leading to ill-posedness are not worse than the two-dimensional ones. (c) 2021 Wiley Periodicals LLC.

引用

页码：1755 / 1797

页数：43

共 33 条

[1]

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

[2] A NOTE ON THE ABSTRACT CAUCHY-KOWALEWSKI THEOREM [J].

ASANO, K .

PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES, 1988, 64 (04) :102-105

[3] Onsager's Conjecture with Physical Boundaries and an Application to the Vanishing Viscosity Limit [J].

Bardos, Claude ;

Titi, Edriss S. ;

Wiedemann, Emil .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2019, 370 (01) :291-310

[4] Mathematics and turbulence: where do we stand? [J].

Bardos, Claude W. ;

Titi, Edriss S. .

JOURNAL OF TURBULENCE, 2013, 14 (03) :42-76

[5]

Collot, 190308244MATHAP

[6]

Collot C., 2018, 180805967MATHAP

[7] NOTE ON LOSS OF REGULARITY FOR SOLUTIONS OF THE 3-D INCOMPRESSIBLE EULER AND RELATED EQUATIONS [J].

CONSTANTIN, P .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1986, 104 (02) :311-326

[8] SEPARATION FOR THE STATIONARY PRANDTL EQUATION [J].

Dalibard, Anne-Laure ;

Masmoudi, Nader .

PUBLICATIONS MATHEMATIQUES DE L IHES, 2019, 130 (01) :187-297

[9] Well-Posedness of the Prandtl Equations Without Any Structural Assumption [J].

Dietert, Helge ;

Gerard-Varet, David .

ANNALS OF PDE, 2019, 5 (01)

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

Gerard-Varet, D. ;

Nguyen, T. .

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

← 1 2 3 4 →