一类带有非线性阻尼项的磁流体动力学方程组的解的整体存在性  

The Global Existence for a Class of Magnetohydrodynamic Equations with Nonlinear Damping Term

作　　者：李林锐[1] 洪明理[1] 郑琳 LI Linrui;HONG Mingli;ZHENG Lin(Basic Courses Department,Institute of Disaster Prevention,Sanhe 065201,China;School of Mathematics and Statistics,North China University of Water Resources and Electric Power,Zhengzhou 450046,China)

机构地区：[1]防灾科技学院基础部,河北三河065201 [2]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《应用数学》2024年第1期63-72,共10页Mathematica Applicata

基　　金：中央高校基本科研业务费专题研究项目(ZY20215116);国家自然科学基金项目(12071192)。

摘　　要：本文研究在多孔介质意义下的一类带有非线性阻尼项a|u|^(α-1)u(a> 0)的不可压的磁流体动力学方程组的解的整体存在性问题,通过古典的能量方法和Sobolev紧性嵌入方法获得了解的整体存在性,利用Gagliardo-Nirenberg插值不等式和其它的一些重要不等式得到了解的正则性结果,建立了弱解和强解的整体存在性,这些结果在很大程度改善了之前相关文献的结果,揭示了磁流体运动的物理现象,为磁流体动力学的发展提供了必要的理论基础.In this paper we consider the global existence results for a new class of magnetohydrodynamic(MHD)equations with nonlinear damping term a|u|^(α-1)u(a>0)in porous media,we obtain the global weak solutions and strong solution by classical energy method and Sobolev compactness embedding method and the regularized results with the aid of Gagliardo-Nirenberg interpolation inequality and the others important inequalities.The results of study improve and extend the ones in the previous works to a large extent,reveal the physical phenomenon of fluid motion,and provide the necessary theoretical basis for the development of magnetohydrodynamic.

关 键 词：磁流体动力学方程组 阻尼项 粘性流 Sobolev紧性嵌入 

分 类 号：O175.29[理学—数学]