TY - JOUR
T1 - Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential
AU - Deng , Dingqun
JO - Communications in Mathematical Analysis and Applications
VL - 4
SP - 421
EP - 468
PY - 2023
DA - 2023/11
SN - 2
DO - http://doi.org/10.4208/cmaa.2023-0008
UR - https://global-sci.org/intro/article_detail/cmaa/22149.html
KW - Vlasov-Poisson-Boltzmann system, regularity, without angular cutoff, regularizing effect, soft potentials.
AB - <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>