三维不可压磁流体方程的整体解

Global solution of 3D incompressible magnetohydrodynamics equations

主要研究带有拉普拉斯耗散和磁扩散的三维磁流体力学系统,在有限能量情形下得到了方程的经典解.选择稳态情形下的Beltrami流作为初值,利用截断函数技术方法和先验估计证明了方程组的整体正则性.

In this paper,a three-dimensional MHD system with both Laplacian dissipation and magnetic diffusion is studied.The classical solutions of the equations are obtained in the case of finite energy.The Beltrami flows in steady state is chosen as the initial value,and the global regularity of the equations for all time is proved by using the cut-off function technique and prior estimation.