Regularity and Decay for Navier-Slip Fluid-Structure Interaction in Exterior Domains

We study the linearized motion of a spherical rigid body immersed in an incompressible viscous fluid occupying the whole space, under Navier slip boundary conditions with friction.

While semigroup regularity and decay estimates are well understood for the no-slip case, such results have been limited to bounded domains in the slip setting.

By exploiting the geometric regularity of the sphere, we establish strong $L^q$-regularity, bounded analyticity, and sharp $ L^q-L^r$ estimates for the corresponding fluid-structure operator.

These results would provide a foundation for constructing strong $W^{2,1}_q$ solutions and Kato-type solutions to the corresponding nonlinear system.