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

作　　者：郭连红 GUO Lianhong(Public Course Teaching Department,Guangzhou Panyu Polytechnic,Guangzhou 511483,China)

机构地区：[1]广州番禺职业技术学院公共课教学部,广东广州511483

出　　处：《应用数学》2025年第2期372-383,共12页Mathematica Applicata

基　　金：2021年度广东省基础与应用基础联合基金青年项目(2021A1515111048);广州番禺职业技术学院2021年科研项目(2021KJ17);2024年广东省教育科学规划课题(2024GXJK920)。

摘　　要：本文研究三维MHD-Boussinesq方程组弱解的正则性问题,运用能量估计方法,结合Gagliardo-Nirenberg插值不等式和Lorentz空间中的一些重要不等式,在Lorentz空间,建立了关于一个速度分量,一个电流密度分量和温度梯度的正则性准则.研究结果表明,在MHD-Boussinesq方程组的正则性理论中,速度场的一个分量起着主导作用. MHD-Boussinesq方程组与MHD方程组及Boussinesq方程组有着紧密联系,所得结果推广了已有相关文献的结论,揭示了在洛伦兹力和热场浮力驱动下不可压导电流体的物理现象.In this paper we consider the regularity problem of the weak solution of the 3D MHDBoussinesq 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 

分 类 号：O175.29[理学—数学]