论文标题
在有限域上不可压缩的MHD方程的消失耗散极限上
On the vanishing dissipation limit for the incompressible MHD equations on bounded domains
论文作者
论文摘要
在本文中，我们研究了有界域中的三维粘性磁磁动力（MHD）方程的溶液对解决方案的溶解度，规律性和消失的耗散极限。在边界上，速度场达到了纳维尔滑动条件，而磁场则满足绝缘条件。结果表明，初始边界问题对于一般平滑域具有全球弱解决方案。更重要的是，对于一个平坦的结构域，我们建立了具有较高级均匀规律性的强溶液的统一局部良好，并且由于耗散趋向于零，因此对理想MHD的溶液的渐近收敛性具有速率。
In this paper, we investigate the solvability, regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magneto-hydrodynamic (MHD) equations in bounded domains. On the boundary, the velocity field fulfills a Navier-slip condition, while the magnetic field satisfies the insulating condition. It is shown that the initial-boundary problem has a global weak solution for a general smooth domain. More importantly, for a flat domain, we establish the uniform local well-posedness of the strong solution with higher order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD as the dissipation tends to zero.
