Temperature Patches for a Generalised 2D Boussinesq System with Singular Velocity

被引：2

作者：

Khor, Calvin ^{[1
,2
]}

Xu, Xiaojing ^{[2
]}

机构：

[1] Beijing Computat Sci Res Ctr, Beijing 100193, Peoples R China

[2] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

来源：

JOURNAL OF NONLINEAR SCIENCE | 2023年 / 33卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Generalized Boussinesq system; Temperature patch; Singular Biot-Savart law; Global Existence; Commutator estimate; GLOBAL WELL-POSEDNESS; SHARP FRONTS; EQUATIONS; REGULARITY; PERSISTENCE; EXISTENCE;

D O I：

10.1007/s00332-022-09886-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove existence and uniqueness of solutions to a modified Boussinesq system with no temperature diffusion, where we modify the Biot-Savart law to make the velocity more singular. Our results are proven for solutions of low regularity, and allows, in particular, the transport of temperature patches with regular boundary. The main new tool is a commutator estimate that requires only a fractional derivative on the velocity.

引用

页数：24

共 41 条

[1] On the global well-posedness for Boussinesq system [J].