三维轴对称不可压MHD方程组弱解的正则性  

Regularity of Weak Solutions of Three Dimensional Axisymmetric Incompressible MHD Equations

作　　者：王玉飞 WANG Yufei(College of Mathematics and Physics,Wenzhou University,Wenzhou,China 325035)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《温州大学学报（自然科学版）》2022年第3期20-27,共8页Journal of Wenzhou University(Natural Science Edition)

摘　　要：研究了在圆柱坐标系下,具有非零旋流分量的三维不可压MHD方程解的正则性.通过计算发现,当三维MHD方程的速度场和磁场的分量满足||(u^(θ)/r,bθ/r)||_(L^(4)(0,T/L^(4)(R^(3)))<∞,或者(r^(θ)u^(θ),r^(θ)b^(θ))∈L^(p)(0,T;L^(q)(R^(3))),2/p+3/q≤1-d时,方程(1)的弱解是光滑的.This paper studies the regularity of solutions of three dimensional incompressible MHD equations with nonzero swirling components in cylinder coordinates.It is found through calculation that the weak solution of the three-dimensional MHD equation is smooth when the velocity field and magnetic field components satisfy ||(u^(θ)/r,bθ/r)||_(L^(4)(0,T/L^(4)(R^(3)))<∞,or(r^(θ)u^(θ),r^(θ)b^(θ))∈L^(p)(0,T;L^(q)(R^(3))),2/p+3/q≤1-d.

关 键 词：MHD方程组 正则性准则 轴对称 

分 类 号：O175.2[理学—数学]