Navier-Stokes-Oseen flows in the exterior of a rotating and translating obstacle

In this paper, we investigate Navier-Stokes-Oseen equation describing flows of incompressible viscous fluid passing a translating and rotating obstacle. The existence, uniqueness, and polynomial stability of bounded and almost periodic weak mild solutions to Navier-Stokes-Oseen equation in the solenoidal Lorentz space \begin{document}$ L^{3}_{σ, w} $\end{document} are shown. Moreover, we also prove the unique existence of time-local mild solutions to this equation in the solenoidal Lorentz spaces \begin{document}$ L^{3,q}_{σ} $\end{document} .