24 citations · 30 across the 6 of their papers we have counts for
6 papers
The Binary-ternary Boltzmann Equation Near Equilibrium
Xianshen Hu, Linjie Xiong, Zhihong Xu
The classical Boltzmann equation, formulated by Boltzmann in 1872, describes the statistical behavior of a dilute gas in a non-equilibrium state. While the global well-posedness of…
Acoustic limit of Boltzmann equations for gas mixture
Gaofeng Wang, Tianfang Wu, Linjie Xiong
In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential . % in the whole space $(x…
The Incompressible Navier-Stokes-Fourier Limit from Boltzmann-Fermi-Dirac Equation
Ning Jiang, Linjie Xiong, Kai Zhou
We study Boltzmann-Fermi-Dirac equation when quantum effects are taken into account in dilute gas dynamics. By employing new estimates on trilinear terms of collision kernels, we p…
Hydrodynamic limits of the kinetic self-organized models
Ning Jiang, Linjie Xiong, Teng-Fei Zhang
The self-organized hydrodynamic models can be derived from the kinetic version of the Vicsek model. The formal derivations and local well-posedness of the macroscopic equations are…
The Vlasov-Poisson-Boltzmann system for the whole range of cutoff soft potentials
Qinghua Xiao, Linjie Xiong, Huijiang Zhao
The dynamics of dilute electrons can be modeled by the fundamental one-species Vlasov-Poisson-Boltzmann system which describes mutual interactions of the electrons through collisio…
Global Existence and Decay of Solutions to the Fokker-Planck-Boltzmann Equation
Linjie Xiong, Tao Wang, Lusheng Wang
The Cauchy problem to the Fokker-Planck-Boltzmann equation under Grad's angular cut-off assumption is investigated. When the initial data is a small perturbation of an equilibrium…