We study the motion of a rigid body in a viscous, compressible fluid filling the exterior of the domain of the solid. The rigid body follows the Newton laws and the fluid is modeled by the Navier–Stokes system. Using a suitable \(L_p-L_q\) approach, we analyze the corresponding coupled system and establish the existence and uniqueness of strong solutions for small initial data, along with their decay rates. In particular, we show that the position of the rigid body converges to a fixed position as \(t\rightarrow \infty \) . To prove our results, we first apply a modified Lagrangian change of variables to rewrite the system in a fixed spatial domain. Then, we analyze the corresponding linear system and prove in particular some \(L_{p}-L_{q}\) decay estimates by adopting a methodology due to Kobayashi and Shibata (Commun Math Phys 200(3):621–659, 1999). Finally, following the recent work of Shibata (J Math Fluid Mech 24(3):Paper No. 66, 2022), we combine these decay estimates with the maximal \(L_{p}\) -regularity of the linear system and with a fixed point argument to obtain both the existence and the decay estimates of solutions for the nonlinear system.
