Weak convergence results for inhomogeneous rotating fluid equations

We consider the equations governing incompressible, viscous fluids in three space dimensions, rotating around an inhomogeneous vectorB(x); this is a generalization of the usual rotating fluid model (whereB is constant). In the case n whichB has non-degenerate critical points, we prove the weak convergence of Leray-type solutions towards a vector field which satisfies a heat equation as the rotation rate tends to infinity. The method of proof uses weak compactness arguments, which also enable us to recover the usual 2D Navier-Stokes limit in the case whenB is constant.