Some qualitative properties of rotating fluids in exterior domains (Q2719463)

The authors discuss the motion of incompressible viscous fluid in rotating system of coordinates with constant angular velocity \(\,\omega/2\,\) [see \textit{H.~P.~Greenspan}, ``The Theory of Rotating Fluids'', Cambridge University Press (1968; Zbl 0182.28103)] NEWLINE\[NEWLINE \begin{gathered} u_t+u\times \omega + u\cdot\nabla u - \nu\Delta u + \nabla p = 0,\\ \nabla\cdot u=0 \end{gathered}\tag{1} NEWLINE\]NEWLINE and the initial and boundary conditions NEWLINE\[NEWLINE \begin{gathered} u(x,0) = u^0(x),\quad x\in\Omega,\\ u(x,t)\big| _{\partial\O mega} = 0,\quad t\in(0,T), \end{gathered}\tag{2} NEWLINE\]NEWLINE where \(\Omega\) is the external part of the domain in \(\mathbb R^3\) with the contact boundary \(\partial\Omega\) being uniform in the class of functions from \(C^3\). The existence conditions are established for strict solutions of the problem (1)\,-\,(2) as well as their regularity.