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The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction. (English) Zbl 1360.35132
Summary: 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 Y. Guo and R. M. Strain [Commun. Math. Phys. 310, No. 3, 649–673 (2012; Zbl 1245.35130)] to the short range interactions.

MSC:
35Q20 Boltzmann equations
83A05 Special relativity
35B40 Asymptotic behavior of solutions to PDEs
35Q83 Vlasov equations
35Q61 Maxwell equations
35B35 Stability in context of PDEs
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