In this paper, we prove a regularity criteria and the local well-posedness of strong solutions to the magnetohydrodynamics with the Hall and ion-slip effects in a smooth bounded domain. Moreover, for the magnetohydrodynamics with the Hall effect and without ion-slip effect, we prove the global stability of strong large solutions. These results are obtained under an integrable property that depends on a new vorticity boundary condition which is motivated by the generalized Navier-slip boundary condition involving the vorticity.

中文翻译：

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具有离子滑移效应的霍尔-磁流体动力学方程的新边界条件

在本文中，我们证明了在光滑有界区域中具有霍尔效应和离子滑移效应的磁流体动力学的正则性准则和强解的局部适定性。此外，对于具有霍尔效应而没有离子滑移效应的磁流体动力学，我们证明了强大解的整体稳定性。这些结果是在取决于新涡旋边界条件的可积性质下获得的，该新涡旋边界条件是由涉及涡旋的广义Navier滑移边界条件引起的。