Wellposedness for anisotropic rotating fluid equations

Abstract

The wellposedness problem for an anisotropic incompressible viscous fluid in ℝ3, rotating around a vector B(t, x):= (b1(t, x), b2(t, x), b3(t, x)), is studied. The global wellposedness in the homogeneous case (B = e3) with sufficiently fast rotation in the space B0,½ is proved. In the inhomogeneous case (B = B(t, xh)), the global existence and uniqueness of the solution in B0, ½ are obtained, provided that the initial data are sufficient small compared to the horizontal viscosity. Furthermore, we obtain uniform local existence and uniqueness of the solution in the same function space. We also obtain propagation of the regularity in B2,1½ under the additional assumption that B depends only on one horizontal space variable.