The Vlasov-Yukawa-Boltzmann system without angular cutoff near vacuum

Abstract

We investigate the global nonlinear stability of the non-cutoff Vlasov-Yukawa-Boltzmann (VYB) system with moderately soft potentials $\gamma +2s\in (0,2)$ and all physically relevant singularity parameter $s\in (0,1)$. Building upon the foundational framework established in Chaturvedi's work [Ann. PDE, 7(2021), no.2, Paper No. 15, 104 pp.], we demonstrate the global nonlinear stability of the VYB system near vacuum by leveraging space-time weights and employing commuting vector fields to achieve integrable time decay for the nonlinear terms. This extends the existence result in Choi and Ha's work [Acta Math. Sci. Ser. B (Engl. Ed.) 35 (2015), no. 4, 887–905.] to angular non-cutoff cases.