Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Propagation of singularities for classical solutions of the Vlasov-Poisson-Boltzmann equation

Pages: 13 - 33, Volume 24, Issue 1, May 2009      doi:10.3934/dcds.2009.24.13

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Laurent Bernis - Université d’Orléans, MAPMO, CNRS, BP 6759, 45067 Orléans Cedex 2, France (email)
Laurent Desvillettes - ENS Cachan, CMLA, IUF & CNRS, PRES UniverSud, 61, Av. du Pdt Wilson, 94235 Cachan Cedex, France (email)

Abstract: In this work, we prove that the singularities (in a fractional Sobolev space) of the classical solutions of the Vlasov-Poisson-Boltzmann equation are propagated along the characteristics of the Vlasov-Poisson equation, and decay exponentially.

Keywords:  Vlasov Equation, Boltzmann Equation, Averaging Lemma, Propagation of Singularities.
Mathematics Subject Classification:  76P05, 35B65, 76X05, 82C40.

Received: June 2007;      Revised: December 2007;      Published: January 2009.