$$L^{p}$$ Theory for the Interaction Between the Incompressible Navier–Stokes System and a Damped Plate

We consider a viscous incompressible fluid governed by the Navier–Stokes system written in domain where part of boundary can deform. assume that corresponding displacement follows damped beam equation. Our main results are existence and uniqueness strong solutions for fluid-structure interaction an $$L^p$$ - $$L^q$$ setting small times or data. An important ingredient proof consists study linear parabolic coupling non stationary Stokes plate show this possesses maximal regularity property proving $${\mathcal {R}}$$ -sectoriality operator. The is then obtained appropriate change variables to handle free fixed point argument treat nonlinearities system.