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Study of dispersive phenomena in geophysical fluids mechanics

Abstract : The introduction is composed by two parts: after a presentation of the geophysical fluids and the principles leading to the primitive equations system and to the quasigeostrophic approximation, we focus on the works done for the primitive equations and the rotating fluids systems. In the second chapter, we formally obtain the asymptotic for the sequence of solutions of the primitive system when the small parameter epsilon goes to zero. This also allows to define the potential vorticity, which we will be crucial in this study. We then study the convergence in the case of the Leray solutions. The third chapter is devoted to the same convergence in the case of solutions in the sense of Fujita and Kato. The last chapter gives more precise informations about the speed of convergence and we also prove a convergence theorem in the case of the vortex patches.
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Contributor : Frédéric Charve <>
Submitted on : Friday, March 11, 2005 - 11:15:09 AM
Last modification on : Wednesday, March 27, 2019 - 4:10:22 PM
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Frédéric Charve. Study of dispersive phenomena in geophysical fluids mechanics. Mathematics [math]. Ecole Polytechnique X, 2004. English. ⟨tel-00008754⟩

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