@Article{CMAA-2-4,
author = {Dingqun, Deng},
title = {Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential},
journal = {Communications in Mathematical Analysis and Applications},
year = {2023},
volume = {2},
number = {4},
pages = {421--468},
abstract = {<p style="text-align: justify;">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 $0&lt;s&lt;1.$ 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 $t&gt;0.$ The proof is based on the time-weighted energy method building upon the pseudo-differential calculus.&nbsp;</p>},
issn = {2790-1939},
doi = {https://doi.org/10.4208/cmaa.2023-0008},
url = {https://global-sci.com/article/81423/global-regularity-of-the-vlasov-poisson-boltzmann-system-near-maxwellian-without-angular-cutoff-for-soft-potential}
}