A priori estimates for free boundary fluid-structure interaction models of magnetohydrodynamic flows with diffusion

Abstract

A 3D free-boundary nonlinear fluid-structure interaction (FSI) problem in which the elastic body fully immersed in the magnetofluid is considered. The fluid is modeled by the Magnetohydrodynamic (MHD) equations with diffusion while the structure is represented by the linear Kirchhoff elastic equation. At the coupling boundary, continuity boundary condition of the Cauchy stress forces and the velocities field as well as the perfect conducting condition for the magnetic field are imposed. A priori estimates in Sobolev norms for the local existence of solutions under the class of initial data is established.