不可压磁流体方程组的一个正则性准则

Regularity Criterion of Incompressible MHD Equations

本文研究了三维不可压MHD方程组轴对称弱解的正则性问题.假定考虑的速度场与磁场均与θ无关,得到了只与速度场有关与磁场无关的正则性条件,即只需速度场旋度的一个分量wθ满足一定的时空可积性条件,解即是光滑的.

In this paper,we investigate the regularity criteria of axisymmetric weak solutions to the three dimensional incompressible MHD equations.By assuming that the velocity field and the magnetic field considered are independent ofθ,we obtain some new regularity conditions which are relevant only to the velocity field independent of the magnetic field.In other words,as long as one component wθof the velocity field curl satisfies a certain space-time integrability condition,the solution is smooth.