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Patterns in partial differential equations arising from fluid mechanics

Abstract : This dissertation is centered around the existence of time–periodic solutions for Hamiltonian models that arise from Fluid Mechanics. In the first part, we explore relative equilibria taking the form of rigid motion (pure rotations or translations) in the plane with uniform and non uniform distributions for standard models like the incompressible Euler equations or the generalized quasi-geostrophic equation. In the second part, we focus on a similar study for the 3D quasi-geostrophic system. The study of this model shows a remarkable diversity compared to the 2D models due to the existence of a large set of stationary solutions or the variety of the associated spectral problems. In the last part, we show some works in progress of this dissertation, and also some conclusions and perspectives.
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Submitted on : Thursday, January 7, 2021 - 2:37:08 PM
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  • HAL Id : tel-03102229, version 1

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Claudia García López. Patterns in partial differential equations arising from fluid mechanics. Analysis of PDEs [math.AP]. Université Rennes 1; Universidad de Granada (Espagne), 2020. English. ⟨NNT : 2020REN1S028⟩. ⟨tel-03102229⟩

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