一类Navier-Stokes-Maxwell方程组的渐近极限问题  

Asymptotic Limit of a Class of Navier-Stokes-Maxwell Equations

作　　者：李林锐[1] LI Lin-rui(Basic Courses Department,Institute of Disaster Prevention,Sanhe 065201,China)

机构地区：[1]防灾科技学院基础部

出　　处：《数学的实践与认识》2018年第24期253-259,共7页Mathematics in Practice and Theory

基　　金：河北省高等学校科学技术研究项目(Z2017047);中央高校基本科研业务费青年教师项目(ZY20180212)

摘　　要：研究了一类Navier-Stokes-Maxwell方程组的渐近极限问题,利用方程的耦合结构,通过采用精细的能量方法、紧性方法、Sobolev嵌入法等,证明了在介电常数γ和抗阻项系数ε趋于零时,带有介电常数和抗阻项的Navier-Stokes-Maxwell方程组的解收敛到古典的二维抛物型的不带有介电常数和抗阻项的磁流体动力学方程组的解,并且给出了相应的收敛率.This paper we study the zero dielectric constant and non-resistive limit of the Navier-Stokes-Maxwell equations,by using the elaborate energy method,compactness and Sobolev embedding method,we prove that the convergences of solutions of the Navier-Stokes- Maxwell system toward to the solutions of the classical 2D parabolic Magnetohydrodynamic equations without dielectric constant and resistive term.Furthermore,the corresponding convergence rates are also obatined.

关 键 词：Navier-Stokes-Maxwell方程组 介电常数 抗阻项 能量方法 Sobolev嵌入 

分 类 号：O175[理学—数学] O361.4[理学—基础数学]