5 citations · 13 across the 7 of their papers we have counts for
7 papers
From two species Vlasov-Maxwell-Boltzmann system to magnetohydrodynamics system
Xu Zhang
In this work, the magnetohydrodynamics system is formally derived from two species Vlasov-Maxwell-Boltzmann system. By employing the hypocoercivity of the linear Boltzmann operator…
The diffusive limits of two species Vlasov-Maxwell-Boltzmann equations
Xu Zhang
In this work, we mainly concern the limiting behavior of the electromagnetic field of two species Vlasov-Maxwell-Botlzmann system in diffusive limits. As knudsen numbers goes to ze…
Sensitivity analysis and incompressible Navier-Stokes-Poisson limit of Vlasov-Poisson-Boltzmann equations with uncertainty
Ning Jiang, Xu Zhang
For the Vlasov-Poisson-Boltzmann equations with random uncertainties from the initial data or collision kernels, we proved the sensitivity analysis and energy estimates uniformly w…
Stability of equilibria to the model for non-isothermal electrokinetics
Ning Jiang, Yi-Long Luo, Xu Zhang
Recently, energetic variational approach was employed to derive models for non-isothermal electrokinetics by Liu et. al \cite{Liu-Wu-Liu-CMS2018}. In particular, the Poisson-Nernst…
Global existence of renormalized solutions to Boltzmann equations with incoming boundary condition and non-cutoff kernel
Ning Jiang, Xu Zhang
We prove the existence of global renormalized solutions to the Boltzmann equation in bounded domain with incoming boundary condition, with non-cutoff collision kernels. Thus we ext…
The Boltzmann equation with incoming boundary condition: global solutions and Navier-Stokes limit
Ning Jiang, Xu Zhang
We consider the Boltzmann equations with cutoff collision kernels in bounded domains. For the initial data with finite physical bounds, we prove the existence of global-in-time ren…
Long time well-posdness of the Prandtl equations in Sobolev space
Chao-Jiang Xu, Xu Zhang
In this paper, we study the long time well-posedness for the nonlinear Prandtl boundary layer equation on the half plane. While the initial data are small perturbations of some mon…