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Optimal large-time decay of the relativistic Landau-Maxwell system. (English) Zbl 1320.35344
J. Differ. Equations 256, No. 2, 832-857 (2014); corrigendum ibid. 258, No. 8, 2966-2967 (2015).
Summary: The Cauchy problem of the relativistic Landau-Maxwell system in \(\mathbb R^{3}\) is investigated. For perturbative initial data with suitable regularity and integrability, we obtain the optimal large-time decay rates of the relativistic Landau-Maxwell system. For the proof, a new interactive instant energy functional is introduced to capture the macroscopic dissipation and the very weak electromagnetic dissipation of the linearized system. The iterative method is applied to handle the time-decay rates of the full instant energy functional because of the regularity-loss property of the electromagnetic field.

35Q75 PDEs in connection with relativity and gravitational theory
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