Existence of local strong solutions for the incompressible viscous and non-resistive MHD-structure interaction model

The purpose of this paper is to study the local well-posedness problem on the magnetohydrodynamics (MHD)-structure interaction (MHDSI) systems. The fluid is represented by the incompressible viscous and non-resistive MHD equation in Euler coordinates while the structure is modeled by the elasticity equation with superconductor material in Lagrangian coordinates. The equations are coupled along the moving interface though transmission boundary conditions for velocity, stress and magnetic field. The local existence of at least one strong solution in time to the incompressible viscous and non-resistive MHD-structure interaction model was proved in the sense of one suitable Sobolev's space norm by using the careful energy method and fixed point theory combining with penalization and regularization techniques and by overcoming the coupling difficulties caused by the magnetic field. (C) 2020 Elsevier Inc. All rights reserved.