Global Solutions and Time Decay of the Non-cutoff Vlasov–Maxwell–Boltzmann System in the Whole Space

Abstract

The global in time classical solutions to the Cauchy problem of the VlasovMaxwell-Boltzmann system near Maxwellians are obtained under the lower regularity index assumption and the weaker smallness condition on the initial perturbation in comparison with the work (Duan et al. in Kinet Relat Models 6(1):159-204, 2013). In particular, we show the relation between time decay rates and spatial derivatives of solutions.Our analysis relies on a refined energy estimates and the interpolation techniques between negative Sobolev norms and positive Sobolev norms without linear decay analysis.

The Boltzmann equation with frictional force for very soft potentials in the whole space

“…−3 < γ < −2. For other kinetic models, such as Vlasov-Poisson(or Maxwell)-Boltzmann systems, Landau-type systems, interested readers can refer to the references [4,5,6,7,8,9,10,11,12,13,18,20,24,27,31] for more details.…”