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Large-Box Transition in Nonlinear Landau Damping for the Vlasov--Yukawa Equation
Ling-Bing He, Yue Luo
We study nonlinear Landau damping for the Vlasov--Yukawa equation in the large-box regime, as a periodic box of length expands to the whole space. First, for , we pro…
Equilibria and linear stability for the Boltzmann equation with radial anharmonic confining potentials
Ling-bing He, Jie Ji, Wu-wei Li
We study the Boltzmann equation in the whole space under the radial anharmonic confining potentials for and for . We first c…
Runaway avalanches in plasmas with external electric fields: spatially inhomogeneous case in a perturbation framework
Ling-Bing He, Richard M. Höfer, Jie Ji +1
We consider the Landau-Coulomb equation for a (hydrogen) plasma heated by an external electric field. In this setting, theoretical and experimental results in plasma physics show t…
Classical limit of the relativistic Vlasov-Maxwell-Landau system
Chuqi Cao, Ling-Bing He, Yuanjie Lei +1
The physical essence of the non-relativistic limit, from the relativistic Vlasov-Maxwell-Landau system to the Vlasov-Poisson-Landau system, lies in the transition from finite-speed…
Boltzmann boundary layer equation with Maxwell reflection boundary condition and applications to fluid limits
Ling-Bing He, Ning Jiang, Yulong Wu
This paper investigates the Knudsen layer equation in half-space, arising from the hydrodynamic limit of the Boltzmann equation to fluid dynamics. We consider the Maxwell reflectio…
Existence, uniqueness and smoothing estimates for spatially homogeneous Landau-Coulomb equation in $H^{-\f12}$ space with polynomial tail
Ling-Bing He, Jie Ji, Yue Luo
We demonstrate that the spatially homogeneous Landau-Coulomb equation exhibits global existence and uniqueness around the space . Additional…
On the Boltzmann equation with soft potentials: Existence, uniqueness and smoothing effect of mild solutions
Ling-Bing He, Jie Ji, Wei-Xi Li
We consider the spatially inhomogeneous Boltzmann equation without angular cutoff for soft potentials. For any given initial datum such that the mass, energy and entropy densities…
On Landau equation with harmonic potential: nonlinear stability of time-periodic Maxwell-Boltzmann distributions
Chuqi Cao, Ling-Bing He, Jie Ji
We provide the first and rigorous confirmations of the hypotheses by Ludwig Boltzmann in his seminal paper \cite{Boltzmann} within the context of the Landau equation in the presenc…