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The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction

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  • We are concerned with the Cauchy problem of the relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. For perturbative initial data with suitable regularity and integrability, we prove the large time stability of solutions to the relativistic Vlasov-Maxwell-Boltzmann system, and also obtain as a byproduct the convergence rates of solutions. Our proof is based on a new time-velocity weighted energy method and some optimal temporal decay estimates on the solution itself. The results also extend the case of ``hard ball" model considered by Guo and Strain [Comm. Math. Phys. 310: 49--673 (2012)] to the short range interactions.
    Mathematics Subject Classification: Primary: 35Q20; Secondary: 83A05, 35B40.

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