JournalsaihpcVol. 2, No. 2pp. 101–118

Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data

  • P. Degond

  • C. Bardos

Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data cover
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Abstract

In this paper we consider the Vlasov Poisson equation in three space variables in the whole space. We show the existence of dispersion property. With this dispersion property we are able to prove the existence of a smooth solution for all times under the following assumption: the initial data are localised and small enough.

Résumé

On considère l’équation de Vlasov Poisson en dimension 3, dans l’espace entier. On dégage une propriété de dispersion. L’utilisation de cette propriété permet de prouver l’existence d’une solution régulière pour tout temps, pourvu que les données initiales soient localisées et assez petites.

Cite this article

P. Degond, C. Bardos, Global existence for the Vlasov-Poisson equation in 3 space variables with small initial data. Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (1985), no. 2, pp. 101–118

DOI 10.1016/S0294-1449(16)30405-X