On a Vlasov–Poisson system in a bounded set with direct reflection boundary conditions

Giorgi, Pierre-Antoine; Nouri, Anne

Annales Henri Lebesgue, Tome 5 (2022), pp. 703-727.

Le système de Vlasov–Poisson modélise un plasma sans collisions. Il est connu que dans un domaine borné des singularités peuvent apparaitre. L’existence globale en temps de solutions continues du système de Vlasov–Poisson est démontrée dans un domaine borné uni-dimensionnel, avec des conditions aux bord de réflexion directe et des données initiales paires par rapport à la vitesse. L’unicité locale en temps est prouvée. Des caractéristiques généralisées sont utilisées. L’électro-neutralité est obtenue à la limite.

The Vlasov–Poisson system models a collisionless plasma. In a bounded domain it is known that singularities can occur. Existence of global in time continuous solutions to the Vlasov–Poisson system is proven in a one-dimensional bounded domain, with direct reflection boundary conditions and initial data even with respect to the $v$-variable. Local in time uniqueness is proven. Generalized characteristics are used. Electroneutrality is obtained in the limit.

Classification : 35Q83, 35A01, 35A02
Mots clés : Vlasov–Poisson system, reflection boundary conditions, generalized characteristics

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