| 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 B00,1/2is proved. In the inhomogeneous case (B=B(t,xh)), the global existence and uniqueness of the solution in B0,1/2are 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 B2,1(?)/2under the additional assumption that B depends only on one horizontal space variable. |
