Nonresonant smoothing for coupled wave and transport equations and the Vlasov-Maxwell system
type: Item
instance of: scholarly article
title: Nonresonant smoothing for coupled wave and transport equations and the Vlasov-Maxwell system
zbMATH Open document ID: 1064.35097
DOI: 10.4171/RMI/409
author: François Bouchut
author: François Golse
author: Christophe Pallard
published in: Revista Matemática Iberoamericana
publication date: 2005-04-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmi/1098885437
full work available at URL: https://eudml.org/doc/39387
review text: Summary: Consider a system consisting of a linear wave equation coupled to a transport equation: \[ \square_{t,x}u=f,\quad (\partial_t+ v(\xi)\cdot \nabla_x)f =P(t,x,\xi,D_\xi)g, \] Such a system is called nonresonant when the maximum speed for particles governed by the transport equation is less than the propagation speed in the wave equation. Velocity averages of solutions to such nonresonant coupled systems are shown to be more regular than those of either the wave or the transport equation alone. This smoothing mechanism is reminiscent of the proof of existence and uniqueness of \(C^1\) solutions of the Vlasov-Maxwell system by \textit{R. Glassey} and \textit{W. Strauss} for time intervals on which particle momenta remain uniformly bounded, in [Arch. Ration. Mech. Anal. 92, 59--90 (1986; Zbl 0595.37072)]. Applications of our smoothing results to solutions of the Vlasov-Maxwell system are discussed.
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 82C40
Mathematics Subject Classification ID: 82D10
zbMATH DE Number: 2156860
zbMATH Keywords: propagation speed
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2156860