Un résultat de diffusion pour l’équation de Hartree autour de solutions non localisées
Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 14, 12 p.

We are interested in the evolution of a system of particles around thermodynamical equilibria presenting an infinite number of particles. That is, we study the asymptotic stability of solutions at equilibrium of the Hartree equation :

itX=-X+w*𝔼(|X|2)X

where X is a random field, w is a real fonction that characterises the interactions between particles, * is the convolution product, and 𝔼 is the expectation. This equation admits solutions whose laws are invariant under temporal and spatial translations, they are thus nonlocalised. We will present their asymtotic stability through a scattering result.

On s’intéresse à l’évolution d’un système de particules autour d’équilibres thermodynamiques présentant un nombre infini de particules. Il s’agit d’étudier la stabilité asymptotique de solutions à l’équilibre de l’équation de Hartree :

itX=-X+w*𝔼(|X|2)X

X est un champ aléatoire, w une fonction réelle qui caractérise les interactions entre particules, * le produit de convolution et 𝔼 est l’espérance. Cette équation admet des solutions dont les lois sont invariantes par translations temporelles et spatiales, elles sont donc non localisées. On exposera leur stabilité asymptotique à travers un résultat de diffusion.

Published online:
DOI: 10.5802/slsedp.123
de Suzzoni, Anne-Sophie 1; Collot, Charles 2

1 Université Paris 13 Sorbonne Paris Cité LAGA, CNRS (UMR 7539) 99, avenue Jean-Baptiste Clément F-93430 Villetaneuse France
2 Department of Mathematics New York University in Abu Dhabi Saadiyat Island P.O. Box 129188 Abu Dhabi United Arab Emirates
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     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
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de Suzzoni, Anne-Sophie; Collot, Charles. Un résultat de diffusion pour l’équation de Hartree autour de solutions non localisées. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 14, 12 p. doi : 10.5802/slsedp.123. http://www.numdam.org/articles/10.5802/slsedp.123/

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