English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We consider the non-cutoff Vlasov-Poisson-Boltzmann (VPB) system of twospecies with soft potential in the whole space $\mathbb{R}^3$ when an initialdata is near Maxwellian. Continuing the work Deng [Comm. Math. Phys. 387,1603-1654 (2021)] for hard potential case, we prove the global regularity ofthe Cauchy problem to VPB system for the case of soft potential in the wholespace for the whole range $0<s<1$. This completes the smoothing effect to theVlasov-Poisson-Boltzmann system, which shows that any classical solutions aresmooth with respect to $(t,x,v)$ for any positive time $t>0$. The proof isbased on the time-weighted energy method building upon the pseudo-differentialcalculus.

Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential