Growth estimates and uniform decay for  a collisionless plasma

Christophe Pallard

doi:10.3934/krm.2011.4.549

Article Contents

2011, Volume 4, Issue 2: 549-567. Doi: 10.3934/krm.2011.4.549

This issue Previous Article Decay property for a plate equation with memory-type dissipation Next Article Asymptotic stability of stationary solutions to the Euler-Poisson equations arising in plasma physics

Growth estimates and uniform decay for a collisionless plasma

Christophe Pallard^1,

1.
Laboratoire de Mathématiques, Université Paris-Sud 11, 91405 Orsay

Received: December 31, 2010

Revised: January 31, 2011

Published: May 2011

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Abstract

We consider the classical Vlasov-Poisson system in three space dimensions in the electrostatic case. For smooth solutions starting from compactly supported initial data, an estimate on velocities is derived, showing an upper bound with a growth rate no larger than $(t\ln t)^{6/25}$. As a consequence, a decay estimate is obtained for the electric field in the $L^\infty$ norm.

Keywords:

Vlasov-Poisson system,
collisionless plasma.

Mathematics Subject Classification: Primary: 82D10; Secondary: 35B40, 76X05.

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