广义磁Boussinesq方程的整体正则性  

Global regularity of generalized MHD-Boussinesq equations

作　　者：杜美华 DU Meihua(Department of Basic,Qingdao West Coast New District Senior Vocational and Technical School,Qingdao 266000,Shandong Province,China)

机构地区：[1]青岛西海岸新区高级职业技术学校基础部,山东青岛266000

出　　处：《浙江大学学报（理学版）》2024年第5期568-571,585,共5页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12371232).

摘　　要：在全空间R^(n)(n≥2)中研究仅具有速度场耗散的广义磁Boussinesq方程的整体适定性。首先,利用方程的结构得到整体解的一致L^(2)界;然后,利用对数型的插值不等式和改进的Gronwall不等式证明了整体解的一致H 1界;最后,利用精细的能量估计,克服方程耗散缺失带来的困难,建立了解的整体一致H^(s)s>1+n/2先验估计,证明了该方程经典解的整体存在唯一性。The purpose of this paper is to study the global well-posedness of generalized MHD-Boussinesq equations with only velocity dissipation in whole space R^(n)(n≥2).Firstly,by exploiting the structure of this system,we obtain the uniform L^(2)-bound of the global solutions.Then,the uniform H 1-bound of the global solutions is proved by making use of logarithmic type interpolation inequality and the improved Gronwall inequality.Finally,by using delicate energy estimates,we overcome the difficulty of lack of dissipation and establish the a priori uniform H^(s)(s>1+n/2)estimate which proves the global existence and uniqueness of the classical solutions to this system.

关 键 词：广义磁Boussinesq方程 部分耗散 整体正则性 

分 类 号：O175.2[理学—数学]