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On considère une équation de Ginzburg-Landau complexe dans le plan. On étudie un régime asymptotique à petit paramètre dans lequel les solutions comportent des singularités ponctuelles, appelées points vortex, et on détermine un système d’équations différentielles ordinaires du premier ordre décrivant la dynamique de ces points jusqu’au premier temps de collision.
Le but de ce texte est de présenter des résultats, en collaboration avec L. Desvillettes et C. Saffirio, à propos de l’existence globale d’une solution pour un système de Vlasov-Poisson avec une charge ponctuelle en dimension trois.
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