A regularity result for the incompressible inviscid magnetohydrodynamics equations in the Arbitrary Lagrangian-Eulerian coordinates

Abstract

Consider herein the incompressible inviscid magnetohydrodynamics equations in a moving domain with free surface boundary conditions. Without smallness assumption in the fluid volume, a priori estimates for solutions of this model are established when the initial data in H2.5+δ (δ>0) upon the Arbitrary Lagrangian-Eulerian coordinates under the boundary condition p+12|B|2=0. Indeed, this is achieved by reformulating the system into a new formulation with the Arbitrary Lagrangian-Eulerian variables, presenting the uniform estimates for the pressure, the tangential estimates for the system, as well as the curl and divergence estimates.