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Documents  Grellier, Sandrine | enregistrements trouvés : 4

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Outreach

Professeur des universités à l'université d'Orléans
Membre du Laboratoire MAPMO
CNRS, Université d'Orléans

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2 y

Research talks

The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform analyticity for a large set of initial data, turbulence phenomenon for a dense set of smooth initial data in large Sobolev spaces.
From joint works with Patrick Gérard.
The cubic Szegö equation has been introduced as a toy model for totally non dispersive evolution equations. It turned out that it is a complete integrable Hamiltonian system for which we built a non linear Fourier transform giving an explicit expression of the solutions.
This explicit formula allows to study the dynamics of the solutions. We will explain different aspects of it: almost-periodicity of the solutions in the energy space, uniform ...

35B40 ; 35B15 ; 35Q55 ; 37K15 ; 47B35

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V

- vi; 112 p.
ISBN 978-2-85629-854-1

Astérisque , 0389

Localisation : Périodique 1er étage

équation de Szegö cubique # système intégrable # équation de Schrödinger non linéaire # opérateur de Hankel # analyse spectrale

35B15 ; 47B35 ; 37K15

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V

- 270 p.
ISBN 978-2-940264-08-7

Monographie de l'Enseignement Mathématique , 0041

Localisation : Ouvrage RdC (THEO)

système dynamique # action de groupes # théorème ergodique # groupe moyennable

37-02 ; 37B05 ; 37A30

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