Asymptotic behavior for the Vlasov-Poisson equations with strong uniform magnetic field and general initial conditions

Mihaï Bostan

doi:10.3934/krm.2020018

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2020, Volume 13, Issue 3: 531-548. Doi: 10.3934/krm.2020018

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Asymptotic behavior for the Vlasov-Poisson equations with strong uniform magnetic field and general initial conditions

Mihaï Bostan

Aix Marseille Université, CNRS, Centrale Marseille, I2M, Centre de Mathématiques et Informatique, UMR 7373, 39 rue Frédéric Joliot Curie, 13453 Marseille Cedex 13, France

Received: June 2019

Published: March 2020

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Abstract

We investigate the Vlasov-Poisson equations perturbed by a strong external uniform magnetic field. We study the asymptotic behavior of the solutions, based on averaging techniques. We analyze the case of general initial conditions. By filtering out the oscillations, we are led to a profile. We prove strong convergence results and establish second order estimates.

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Mathematics Subject Classification: Primary: 35Q75, 78A35; Secondary: 82D10.

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