Regularity results in 2D fluid–structure interaction

Abstract We study the interaction of an incompressible fluid in two dimensions with elastic structure yielding moving boundary physical domain. The displacement is described by a linear viscoelastic beam equation. Our main result existence unique global strong solution. Previously, only ideal case flat reference geometry was considered such that can move vertical direction. allow for general geometric set-up, where even occupy complete boundary. tool—being independent interest—is maximal regularity estimate steady Stokes system domains minimal regularity. In particular, we control velocity field $$W^{2,2}$$ W 2 , terms forcing $$L^2$$ L provided belongs roughly to $$W^{3/2,2}.$$ 3 / . This applied momentum equation domain (for fixed time) material derivative as right-hand side. Since priori class $$W^{2,2},$$ known results do not apply here they require $$C^2$$ C -boundary.