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Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System

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Abstract

In the study of solutions to the relativistic Boltzmann equation, their regularity with respect to the momentum variables has been an outstanding question, even local in time, due to the initially unexpected growth in the post-collisional momentum variables which was discovered in 1991 by Glassey & Strauss (Transport Theory Stat Phys 20(1):55–68, 1991). We establish momentum regularity within energy spaces via a new splitting technique and interplay between the Glassey-Strauss frame and the center of mass frame of the relativistic collision operator. In a periodic box, these new momentum regularity estimates lead to a proof of global existence of classical solutions to the two-species relativistic Vlasov-Maxwell-Boltzmann system for charged particles near Maxwellian with hard ball interaction.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, Providence, RI, 02912, USA

    Yan Guo

  2. Department of Mathematics, David Rittenhouse Lab, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA, 19104, USA

    Robert M. Strain

Authors
  1. Yan Guo
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  2. Robert M. Strain
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Corresponding author

Correspondence to Robert M. Strain.

Additional information

Communicated by H. Yau

Y.G. was partially supported by the NSF grant DMS-0905255, a NSF FRG grant, and the Chinese NSF grant # 10828103.

R.M.S. was partially supported by the NSF grant DMS-0901463, and an Alfred P. Sloan Foundation Research Fellowship.

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Guo, Y., Strain, R.M. Momentum Regularity and Stability of the Relativistic Vlasov-Maxwell-Boltzmann System. Commun. Math. Phys. 310, 649–673 (2012). https://doi.org/10.1007/s00220-012-1417-z

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  • DOI: https://doi.org/10.1007/s00220-012-1417-z

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