DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field

P. E. Jabin, N. Masmoudi

Research output: Contribution to journalArticle

Abstract

We show the existence and uniqueness of a DiPerna–Lions flow for relativistic particles subject to a Lorentz force in an electromagnetic field. The electric and magnetic fields solve the linear Maxwell system in the vacuum but for singular initial conditions which are only in the physical energy space. As the corresponding force field is only in L<sup>2</sup>, we have to perform a careful analysis of the cancellations over a trajectory.

Original languageEnglish (US)
Pages (from-to)1029-1067
Number of pages39
JournalArchive for Rational Mechanics and Analysis
Volume217
Issue number3
DOIs
StatePublished - Feb 20 2015

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Lorentz force
Maxwell System
Force Field
Cancellation
Electromagnetic fields
Electromagnetic Fields
Electric Field
Vacuum
Existence and Uniqueness
Initial conditions
Magnetic Field
Linear Systems
Electric fields
Trajectories
Trajectory
Magnetic fields
Energy

ASJC Scopus subject areas

  • Analysis
  • Mechanical Engineering
  • Mathematics (miscellaneous)

Cite this

DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field. / Jabin, P. E.; Masmoudi, N.

In: Archive for Rational Mechanics and Analysis, Vol. 217, No. 3, 20.02.2015, p. 1029-1067.

Research output: Contribution to journalArticle

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