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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 L 2, we have to perform a careful analysis of the cancellations over a trajectory.

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Authors and Affiliations

  1. CSCAMM and Dpt of Mathematics, Univ. of Maryland, College Park, MD, 20742-4015, USA

    P.-E. Jabin

  2. Courant Institute, 251 Mercer St, New York, NY, 10012, USA

    N. Masmoudi

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  1. P.-E. Jabin
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  2. N. Masmoudi
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Correspondence to P.-E. Jabin.

Additional information

Communicated by L. Saint-Raymond

N. Masmoudi is partially supported by an NSF Grant DMS-1211806, P.-E. Jabin by NSF Grant 1312142 and by NSF Grant 1107444.

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Jabin, PE., Masmoudi, N. DiPerna–Lions Flow for Relativistic Particles in an Electromagnetic Field. Arch Rational Mech Anal 217, 1029–1067 (2015). https://doi.org/10.1007/s00205-015-0850-5

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  • DOI: https://doi.org/10.1007/s00205-015-0850-5

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