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Heat Flows with Prescribed Singularities from 3-dimensional Manifold
Jie Ji, Jingru Niu
In this paper, we study singular heat flows from a 3-dimensional complete bounded Riemannian manifold without boundary into the hyperbolic space with prescribe singularity along a…
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…