Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

Details Uniform Local Existence for Inhomogeneous Rotating Fluid Equations Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

2008-06-28

arxiv.org/abs/0806.4658v1

Mathematics

Analysis of PDEs

25 pages, to appear in Journal of Dynamics and Differential Equations

Scientific paper

10.1007/s10884-008-9120-7

We investigate the equations of anisotropic incompressible viscous fluids in $\R^3$, rotating around an inhomogeneous vector $B(t, x_1, x_2)$. We prove the global existence of strong solutions in suitable anisotropic Sobolev spaces for small initial data, as well as uniformlocal existence result with respect to the Rossby number in the same functional spaces under the additional assumption that $B=B(t,x_1)$ or $B=B(t,x_2)$. We also obtain the propagation of the isotropic Sobolev regularity using a new refined product law.

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