Compressible Hall magnetohydrodynamic systems in three-dimensional bounded regions

In order to make the global existence and asymptotic properties of the strong solution of the magnetohydrodynamic system more general, and better describe the properties of the system in three-dimensional space. It is mainly by using the method of energy estimation to obtain the global existence and asymptotic nature of the strong solution of the system. Firstly, the local existence of the system is given, and then the prior estimation of the system within the region and near the boundary is given, basing on the fine energy estimation within the region and near the boundary, the truncation function and the finite coverage method are used to level the boundary region, and finally the proposed theorem is proved in three steps by combining the local existence. Basing on this, the global existence, uniqueness and exponential convergence speed estimation of the strong solution in the bounded domain are obtained. For the three-dimensional compressible Hall magnetohydrodynamic system, the global existence and asymptotic properties of the system in the bounded region with smooth boundaries are proved, and the problem that the spatial derivative at the boundary cannot be estimated by the classical energy method is solved.