On the motion of a small rigid body in a viscous compressible fluid

Abstract We consider the motion of a small rigid object immersed in a viscous compressible fluid in the 3-dimensional Eucleidean space. Assuming the object is a ball of a small radius ε we show that the behavior of the fluid is not influenced by the object in the asymptotic limit The result holds for the isentropic pressure law for any under mild assumptions concerning the rigid body density. In particular, the latter may be bounded as soon as The proof uses a new method of construction of the test functions in the weak formulation of the problem, and, in particular, a new form of the so-called Bogovskii operator.