$$L^p$$-strong solution to fluid-rigid body interaction system with Navier slip boundary condition

We study a fluid-structure interaction problem describing movement of rigid body inside bounded domain filled by viscous fluid. The fluid is modelled the generalized incompressible Naiver–Stokes equations which include cases Newtonian and non-Newtonian fluids. are coupled via Navier slip boundary conditions balance forces at fluid-rigid interface. Our analysis also includes case nonlinear condition. main results assert existence strong solutions, in an $$L^p-L^q$$ setting, globally time, for small data case, while solutions $$L^p$$ -spaces, locally obtained case. proof essentially uses maximal regularity property associated linear system proving $${\mathcal {R}}$$ -sectoriality corresponding operator. result general fluid-solid then relies upon previous Moreover, we prove exponential stability