Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential
Year: 2023
Author: Dingqun Deng
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 4 : pp. 421–468
Abstract
We consider the non-cutoff Vlasov-Poisson-Boltzmann (VPB) system of two species with soft potential in the whole space $\mathbb{R}^3$ when an initial data is near Maxwellian. Continuing the work Deng [Comm. Math. Phys. 387 (2021)] for hard potential case, we prove the global regularity of the Cauchy problem to VPB system for the case of soft potential in the whole space for the whole range $0<s<1.$ This completes the smoothing effect of the Vlasov-Poisson-Boltzmann system, which shows that any classical solutions are smooth with respect to $(t,x,v)$ for any positive time $t>0.$ The proof is based on the time-weighted energy method building upon the pseudo-differential calculus.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmaa.2023-0008
Communications in Mathematical Analysis and Applications, Vol. 2 (2023), Iss. 4 : pp. 421–468
Published online: 2023-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 48
Keywords: Vlasov-Poisson-Boltzmann system regularity without angular cutoff regularizing effect soft potentials.