Global solutions and exponential time decay rates to the Navier–Stokes–Vlasov–Fokker–Planck system in low regularity space

Abstract

In this paper, we show that the mild solutions to the Navier–Stokes–Vlasov–Fokker–Planck system exist globally in time near a global Maxwellian, provided that we take small-amplitude initial data in the function space Lk1LT∞Lv2. As a product, we also get the exponential time decay rates for the solutions. Our analysis relies on the refined energy estimates and the low regularity function space Lk1LT∞Lv2 introduced by the work in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)].