DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field

P. E. Jabin; N. Masmoudi

doi:10.1007/s00205-015-0850-5

DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field

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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 L², we have to perform a careful analysis of the cancellations over a trajectory.

Original language	English (US)
Pages (from-to)	1029-1067
Number of pages	39
Journal	Archive for Rational Mechanics and Analysis
Volume	217
Issue number	3
DOIs	https://doi.org/10.1007/s00205-015-0850-5
State	Published - Sep 17 2015

ASJC Scopus subject areas

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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title = "DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field",

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 L2, we have to perform a careful analysis of the cancellations over a trajectory.",

author = "Jabin, {P. E.} and N. Masmoudi",

note = "Funding Information: N. Masmoudi is partially supported by an NSF Grant DMS-1211806, P.-E. Jabin by NSF Grant 1312142 and by NSF Grant 1107444. Publisher Copyright: {\textcopyright} 2015, Springer-Verlag Berlin Heidelberg.",

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AU - Masmoudi, N.

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N2 - 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 L2, we have to perform a careful analysis of the cancellations over a trajectory.

AB - 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 L2, we have to perform a careful analysis of the cancellations over a trajectory.

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DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field

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