有界域上具有部分耗散和磁扩散的二维磁流体方程的全局适定性

Global Well-posedness for the 2D MHD System with Partial Dissipation and Magnetic Diffusion in a Bounded Domain

探究了具有部分耗散和磁扩散的二维不可压缩磁流体(MHD)方程的初边值问题.在有界区域上,当系统的各个方向上的耗散系数和磁扩散系数都非负时,我们得到了该模型的强解是整体存在且唯一的.此外,对周期域而言,其解仍是全局适定的.

We consider the initial boundary value problem of the two-dimensional incompressible magnetohydrodynamic(MHD) equations with partial dissipation and magnetic diffusion.The global and unique strong solution of the model in a bounded domain is justified when the dissipation and magnetic diffusion coefficient in all directions are nonnegative.In addition,the global well-posedness of the system can be extended into the periodic boundary.