Well-posedness for incompressible fluid–solid interaction with vorticity

Abstract

This paper is concerned with the global well-posedness of a fluid–solid interaction model with vorticity which can be written as hyperbolic–parabolic coupled system along the conjugate boundary through the balance of velocity and flux, where the fluid is governed by the incompressible Navier–Stokes equation with vorticity while the elastic solid is modeled by wave equation. The global existence of weak solution to the fluid–solid coupled system is proved by using the energy method and delicate estimates while the uniqueness is illustrated by the truncation-polishing technique to overcome the lack of smoothness for the coupled system in the variational form.