The steady motion of a Navier-Stokes liquid around a rigid body

Let (ProQuest: Formulae and/or non-USASCII text omitted; see image) be a body moving by prescribed rigid motion in a Navier-Stokes liquid (ProQuest: Formulae and/or non-USASCII text omitted; see image) that fills the whole space and is subject to given boundary conditions and body force. Under the assumptions that, with respect to a frame (ProQuest: Formulae and/or non-USASCII text omitted; see image) , attached to (ProQuest: Formulae and/or non-USASCII text omitted; see image) , these data are time independent, and that their magnitude is not "too large", we show the existence of one and only one corresponding steady motion of (ProQuest: Formulae and/or non-USASCII text omitted; see image) , with respect to (ProQuest: Formulae and/or non-USASCII text omitted; see image) , such that the velocity field, at the generic point x in space, decays like |x|^sup -1^. These solutions are "physically reasonable" in the sense of FINN [10]. In particular, they are unique and satisfy the energy equation. Among other things, this result is relevant in engineering applications involving orientation of particles in viscous liquid [14].[PUBLICATION ABSTRACT]