ON THE DEGENERATE BOUSSINESQ EQUATIONS ON SURFACES

被引：1

作者：

Li, Siran ^{[1
,2
]}

Wu, Jiahong ^{[3
]}

Zhao, Kun ^{[4
]}

机构：

[1] Rice Univ, Dept Math, MS 136 POB 1892, Houston, TX 77251 USA

[2] McGill Univ, Dept Math, Burnside Hall,805 Sherbrooke St West, Montreal, PQ, Canada

[3] Oklahoma State Univ, Dept Math, 401 Math Sci, Stillwater, OK 74078 USA

[4] Tulane Univ, Dept Math, 6823 St Charles Ave, New Orleans, LA 70118 USA

来源：

JOURNAL OF GEOMETRIC MECHANICS | 2020年 / 12卷 / 01期

关键词：

Boussinesq Equations; Strong Solution; Closed Surfaces; Well-posedness; Breakdown Criteria; Vanishing Viscosity Limit; Vanishing Diffusivity Limit; GLOBAL WELL-POSEDNESS; BLOW-UP CRITERION; QUASI-GEOSTROPHIC EQUATION; EULER EQUATIONS; LOCAL EXISTENCE; WEAK SOLUTIONS; NAVIER-STOKES; REGULARITY; SYSTEM;

D O I：

10.3934/jgm.2020006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the non-degenerate and partially degenerate Boussinesq equations on a closed surface Sigma. When Sigma has intrinsic curvature of finite Lipschitz norm, we prove the existence of global strong solutions to the Cauchy problem of the Boussinesq equations with full or partial dissipations. The issues of uniqueness and singular limits (vanishing viscosity/vanishing thermal diffusivity) are also addressed. In addition, we establish a breakdown criterion for the strong solutions for the case of zero viscosity and zero thermal diffusivity. These appear to be among the first results for Boussinesq systems on Riemannian manifolds.

引用

页码：107 / 140

页数：34

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