Decay rates of the highest order spatial derivatives for solutions of compressible Hall MHD system with or without Coulomb force

Abstract

In this thesis, we study the decay rates of the highest order (M-th order) spatial derivatives for solutions of both compressible Hall MHD system and that with Coulomb force by a pure energy method inspired by Guo and Wang (2012)[12] and Gao, Li and Yao (2023)[9]. When the norm of H3 for the initial perturbation is small enough, and the norms of both HM(M≥3) and H˙−α(α∈[0,32)) for that only need to be bounded, we first prove the decay rates of compressible Hall MHD system in L2 are (1+t)−(M+α)2. And then affected by the Coulomb force, for compressible Hall MHD system with Coulomb force, we obtain the decay rates are (1+t)−(M+α)2 for α∈[12,32) and (1+t)12[(14−12α)−(M+α)] for α∈[0,12), which are consistent with the decay estimates for compressible MHD system with Coulomb force. In particular, the results improve the original decay rates (1+t)−(M−1+α)2 established by Xu et al. (2016)[46] and Tan, Tong and Wang (2015)[31].