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Régularité et asymptotique pour les équations primitives

Abstract : This thesis, containing four chapters, studies the existence, uniqueness and regularity of the solutions of the Primitive Equations (PEs) of the oceans and the atmosphere in space dimensions 2 and 3 (Chapters 1--3), and also the asymptotic behavior of the PEs when the Rossby number goes to zero (Chapter 4); the boundary conditions considered here are periodical.

In the first chapter, we consider the PEs of the ocean in a two-dimensional space (three dimensional motion independent of the y variable). We prove the existence, globally in time, of a weak solution and the existence and uniqueness of strong solutions. Moreover, we prove the existence of more regular solutions, up to C-infinity regularity.

In the second chapter, for a model similar to the previous one, we prove that, for a forcing term which is analytical in time with values in a Gevrey space, the solutions of the PEs starting with the initial data in a certain Sobolev space become, for some positive time, elements of a certain Gevrey class.

As a natural continuation of the work from the first two chapters, in the third chapter we consider the PEs in a 3D domain and we study the Sobolev and Gevrey regularity for the solutions.

The last chapter of the thesis is devoted to the study of the asymptotic behavior when the Rossby number goes to zero, for the PEs in the form considered in the first chapter. The aim of this work is to average, using the renormalization group method, the oscillations of the exact solution when the Rossby number goes to zero, and to prove that the averaged solution is a good approximation of the exact oscillating solution.
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Contributor : Madalina Elena Petcu Connect in order to contact the contributor
Submitted on : Sunday, March 19, 2006 - 10:58:17 PM
Last modification on : Sunday, June 26, 2022 - 11:45:39 AM
Long-term archiving on: : Monday, September 17, 2012 - 12:41:17 PM



  • HAL Id : tel-00011982, version 1



Madalina Elena Petcu. Régularité et asymptotique pour les équations primitives. Mathématiques [math]. Université Paris Sud - Paris XI, 2005. Français. ⟨tel-00011982⟩



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