Analytic solutions to a strongly nonlinear Vlasov equation

Pierre-Emmanuel Jabin; A. Nouri

doi:10.1016/j.crma.2011.03.024

Partial Differential Equations/Mathematical Physics

Analytic solutions to a strongly nonlinear Vlasov equation

Presented by: the Editorial Board

Pierre-Emmanuel Jabin ¹; A. Nouri ²

¹ Laboratoire Dieudonné, University of Nice-Sophia Antipolis, parc Valrose, 06000 Nice, France
² Aix-Marseille University, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 541-546.

Abstract
Résumé

We prove the existence for short times of analytic solutions to a Vlasov type equation. The corresponding model is one-dimensional but uses a quite singular force term which involves a full derivative in x of the macroscopic density, making the existence of solutions a difficult question.

Nous démontrons lʼexistence en temps petit de solution analytique à une équation de type Vlasov. Le modèle considéré est mono-dimensionnel mais le terme de force correspondant fait intervenir une dérivée complète de la densité macroscopique. Ceci rend la question de lʼexistence de solution particulièrement délicate.

Received: 2011-03-15
Accepted: 2011-03-29
Published online: 2011-04-12

DOI: 10.1016/j.crma.2011.03.024

Author's affiliations:

Pierre-Emmanuel Jabin ¹; A. Nouri ²

¹ Laboratoire Dieudonné, University of Nice-Sophia Antipolis, parc Valrose, 06000 Nice, France
² Aix-Marseille University, France

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     title = {Analytic solutions to a strongly nonlinear {Vlasov} equation},
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     language = {en},
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Pierre-Emmanuel Jabin; A. Nouri. Analytic solutions to a strongly nonlinear Vlasov equation. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 541-546. doi : 10.1016/j.crma.2011.03.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.024/

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