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Theses

On the stability of Spherically symmetric travelling waves and the motion of a fluid between two infinte plates

Abstract : This thesis deals with the asymptotic behavior of global solutions of evolution parabolic semilinear Partial Differential Equations. Through two different examples, we study the convergence of solutions, when time goes to infinity, towards particular solutions (travelling waves, self-similar solutions). On the one hand, we study the asymptotic stability of spherically symmetric travelling waves in a scalar reaction-diffusion equation with bistable nonlinearity. We get a stability result for small radial perturbations and an instability one for arbitrary (i.e. non-symmetric) perturbations. On the other hand, we compute an asymptotic development up to second order of solutions with small initial data of Navier-Stokes and Navier-Stokes Coriolis equations in a three-dimensional layer. In particular, we show that their behaviors are governed by the Oseen Vortex. We then generalise this result to any global solution uniformly bounded in time, with no more smallness assumption on the initial data. Finally, we highlight such solutions for the Navier-Stokes Coriolis equation in case of a sufficiently high rotation.
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https://tel.archives-ouvertes.fr/tel-00004854
Contributor : Violaine Roussier-Michon <>
Submitted on : Wednesday, February 18, 2004 - 5:37:37 PM
Last modification on : Tuesday, May 7, 2019 - 6:30:09 PM
Long-term archiving on: : Friday, April 2, 2010 - 7:43:48 PM

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  • HAL Id : tel-00004854, version 1

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Violaine Roussier-Michon. On the stability of Spherically symmetric travelling waves and the motion of a fluid between two infinte plates. Mathematics [math]. Université Paris Sud - Paris XI, 2003. English. ⟨tel-00004854⟩

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