应用数学2025，Vol.38Issue(2)：372-383,12.
三维MHD-Boussinesq方程组在Lorentz空间中的正则性准则
Regularity Criteria for the Three-Dimensional MHD-Boussinesq Equations in Lorentz Space
摘要
Abstract
In this paper we consider the regularity problem of the weak solution of the 3D MHD-Boussinesq equations.By classical energy method and Gagliardo-Nirenberg interpolation inequality and the others important inequalities,we obtain a regularity criterion for a velocity component,a current density component and a temperature gradient in Lorentz space.This result suggests that a component of the velocity field plays a dominant role in the regularity theory of the system of MHD-Boussinesq equations.MHD-Boussinesq equations are closely related to MHD and Boussinesq equations.The results of study improve and extend the ones in the previous works,and reveal the physical phenomenon of noncompressible conductive fluid driven by Lorentz force and thermal field buoyancy.关键词
MHD-Boussinesq系统/弱解正则性/能量估计/Lorentz空间Key words
MHD-Boussinesq system/Regularity of weak solution/Energy estimate/Lorentz space分类
数学引用本文复制引用
郭连红..三维MHD-Boussinesq方程组在Lorentz空间中的正则性准则[J].应用数学,2025,38(2):372-383,12.基金项目
2021年度广东省基础与应用基础联合基金青年项目(2021A1515111048) （2021A1515111048）
广州番禺职业技术学院2021年科研项目(2021KJ17) （2021KJ17）
2024年广东省教育科学规划课题(2024GXJK920) （2024GXJK920）
