Global mild solutions of the non-cutoff Vlasov–Poisson–Boltzmann system

Abstract

This paper is concerned with the Cauchy problem on the Vlasov–Poisson–Boltzmann system in the torus domain. The Boltzmann collision kernel is assumed to be angular non-cutoff with $0 \leq \gamma \lt 1$ and $1/2 \leq s \lt 1$, where $\gamma, s$ are two parameters describing the kinetic and angular singularities, respectively. We obtain the global-in-time unique mild solutions, and prove that the solutions converge to the global Maxwellian with the large-time decay rate of $\mathcal{O}(e^{-\lambda t})$ in the $L^1_k L^2_v$-norm for some $\lambda \gt 0$. Furthermore, we justify the property of propagation of regularity of solutions in the spatial variable.