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

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+& delta; (& delta; > 0) upon the Arbitrary Lagrangian-Eulerian coordinates under the boundary condition p + 21 |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.& COPY; 2023 Elsevier Inc. All rights reserved.