Uniform Local Existence for Inhomogeneous Rotating Fluid Equations |
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Authors: | Mohamed Majdoub Marius Paicu |
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Institution: | (1) Département de Mathématiques, Faculté des Sciences de Tunis, Campus Universitaire, 1060 Tunis, Tunisia;(2) Département de Mathématiques, Université de Paris-Sud, Batiment 425, Orsay, France |
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Abstract: | We investigate the equations of anisotropic incompressible viscous fluids in , 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 uniform local 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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Keywords: | Inhomogeneous rotating fluids Anisotropic viscosity Local existence |
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