The Navier-Stokes flow in the exterior of rotating obstacles

In this note we describe recent results on the equations of Navier-Stokes in the exterior of a rotating domain. After rewriting the problem on a fixed exterior domain Omega in R-n, it is shown that for initial data u(0) epsilon L-sigma(p)(Omega) with p >= n and which are satisfying a certain compatibility condition there exists a unique local mild solution to the Navier-Stokes problem. In the case of the whole space of R-n, this local mild solution is even analytic in the space variable x.