Analyticity of the semigroup associated with the fluid–rigid body problem and local existence of strong solutions

In this paper, we study the linear operator associated with the fluid–rigid body problem. The operator was first introduced by T. Takahashi and M. Tucsnak (2004) [22]. For the general three-dimensional case, we prove that the corresponding semigroup is analytic on (p⩾2). In particular, when the solid is a ball in R3, the corresponding semigroup is analytic on L2(R3)∩Lp(R3) (p⩾6). And for this case, a unique local strong solution to the fluid–rigid body problem is derived.