Well‐Posedness of the Fluid–Structure Interactions Problem for Magnetofluid in the Flat Domain

ABSTRACT A 2D nonlinear fluid–structure interaction (FSI) problems in which the elastic body fully immersed in the magnetofluid is considered. The coupling takes place on the interface via the continuity of the normal components of the Cauchy stress tensor and the displacement (or velocity). First, a divergence‐free weak solution that is an auxiliary, equivalent formulation to the solution of FSI problem is introduced. Then, based on Galerkin approximations and energy estimates, the global‐in‐time existence of the weak solution is obtained. Further, the regularity on time and space derivatives of weak solution is established by using the estimates on fractional tangential derivative. Finally, the uniqueness is proved under additional assumptions on the data.