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Large-time behavior for fluid and kinetic plasmas with collisions. (English) Zbl 1341.35095

Summary: The motion of collisional plasmas can be governed either by the Euler-Maxwell system with damping at the fluid level or by the Vlasov-Maxwell-Boltzmann system at the kinetic level. In the note, we present some recent results in [the author et al., Math. Models Methods Appl. Sci. 25, No. 11, Article ID 2089, 2089–2151 (2015; Zbl 1330.35318); SIAM J. Math. Anal. 47, No. 5, 3585–3647 (2015; Zbl 1326.35221)] for the study of the non-trivial large-time behavior of solutions to the Cauchy problem on the related models in perturbation framework.

MSC:

35Q20 Boltzmann equations
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35Q61 Maxwell equations
35Q83 Vlasov equations
76X05 Ionized gas flow in electromagnetic fields; plasmic flow
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