2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210538We investigate the equations of anisotropic axisymmetric incompressible viscous fluids in the exterior of a cylinder of $\R^3$, rotating around an inhomogeneous vector $B(t, r)$. We prove uniform local existence with respect to the Rossby number in suitable anisotropic Sobolev spaces. We also obtain the propagation of the isotropic Sobolev regularity.SubmittedAnalysis of PDEs35-xx, 35Qxx, 35Q30text