论文标题
加权$ l^2 $空间中的弱唯一性和MHD方程的本地Morrey空间中的弱解决方案
Weak-strong uniqueness in weighted $L^2$ spaces and weak suitable solutions in local Morrey spaces for the MHD equations
论文作者
论文摘要
我们在这里考虑整个空间上的磁性流动力学（MHD）方程。对于3D情况，在加权$ l^2 $空间的设置中，我们获得了一个弱的唯一性标准，前提是速度场和磁场属于相当通用的乘数空间。另一方面，我们研究了用于间歇性初始数据的局部和全球存在的局部和全球存在，这是通过局部莫雷空间来表征的。在3D Navier-Stokes方程的背景下，在当代作品中也展示了这个较大的初始数据空间。最后，我们在第二案例中就本地和全球存在问题进行了讨论。
We consider here the magneto-hydrodynamics (MHD) equations on the whole space. For the 3D case, in the setting of the weighted $L^2$ spaces we obtain a weak-strong uniqueness criterion provided that the velocity field and the magnetic field belong to a fairly general multipliers space. On the other hand, we study the local and global existence of weak suitable solutions for intermittent initial data, which is characterized through a local Morrey space. This large initial data space was also exhibit in a contemporary work [4] in the context of 3D Navier-Stokes equations. Finally, we make a discussion on the local and global existence problem in the 2D case.
