Global well-posedness of a new class of initial-boundary value problem on incompressible MHD/MHD-Boussinesq equations

Abstract

The global well-posedness of a new class of initial-boundary value problem on incompressible MHD equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD equation with the given pressure-velocity's relation boundary condition for the fluid field at the boundary and with one perfectly insulating boundary condition for the magnetic field at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also established. The corresponding results are also extended to the two/three-dimensional incompressible MHD-Boussinesq equations with the density-velocity's relation boundary condition for the density.