We consider the initial value problem for the Navier–Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data in the scaling-invariant space when the speed of rotation is sufficiently high. Furthermore, we consider the asymptotic limit of the fast rotation and show that the global solution converges to that of 2D incompressible Navier–Stokes equations in some global in time space-time norms.
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)