Some remarks on the steady fall of a rigid body in viscous fluids.

The study of the motion of small particles in a viscous liquid has become one of the main focuses of the applied research over the last 40 years. To understand the problem, the linearized case was investigated. It leads to solving the Stokes or the Oseen problems with additional terms $(\omega \times x)\cdot \nabla u$ and $\omega \times u$. In this talk we consider the following model \[\begin{align*} & -\mu \Delta v + v\cdot \nabla v +\omega \times v + \nabla p = f \quad\text{ in  }\Omega,\\ & \nabla\cdot v=0\quad\text{ in }\Omega,\\ & v|_{\partial \Omega } =v_{*},\\ & \lim_{|x| \to \infty } v=v_{\infty}, \end{align*}\] where $\Omega$ is the whole space $\mathbb{R}^3$ or an exterior domain in $\mathbb{R}^3$ and $\omega \times v $ is the Coriolis force. We prove the existence and uniqueness of strong solutions to this problem.