Navier-Stokes flow past a translating body: attainability of the steady state as limit of an $L^p$ weak solution

Consider a viscous, incompressible, Newtonian fluid that fills the region of space exterior to a rigid body. Let the fluid be activated by a perturbation $u_0\in L^p(\OO)$, $p\in (2,3)$ and let the body start to translate with a prescribed velocity $-h(t)u_\infty$, $t>0$, $u_\infty\in\R^3\setminus \