127 citations · 324 across the 42 of their papers we have counts for
49 papers
Sharp Regularizing Effect of the Cauchy Problem for the Inhomogeneous Non-Cutoff Kac Equation
Xinzhi Cai, Hongmei Cao, Chao-jiang Xu
In this work, we study the spatially inhomogeneous Kac equation with a non-cutoff cross section in a setting close to equilibrium. We prove that the solution to the Cauchy problem…
Sharp regularization effect for the non-cutoff Boltzmann equation with hard potentials
Jun-Ling Chen, Wei-Xi Li, Chao-Jiang Xu
For the Maxwellian molecules or hard potentials case, we verify the smoothing effect for the spatially inhomogeneous Boltzmann equation without angular cutoff. Given initial data w…
Long-time existence of Gevrey-2 solutions to the 3D Prandtl boundary layer equations
Xinghong Pan, Chao-Jiang Xu
For the three dimensional Prandtl boundary layer equations, we will show that for arbitrary and sufficiently small , the lifespan of the Gevrey-2 solution is at least of siz…
Regularity of the spatially homogenous fractional Kramers-Fokker-Planck equation
Chao-Jiang Xu, Yan Xu
We study the Cauchy problem of the spatially homogenous fractional Kramers-Fokker-Planck equation and show that the solution enjoys Gevrey regularity and decay estimation with an L…
A remark about time-analyticity of the linear Landau equation with soft potential
Chao-Jiang Xu, Yan Xu
In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy problem enjoys the anal…
Analytic Gelfand-Shilov smoothing effect of the spatially homogeneous Landau equation
Hao-Guang Li, Chao-Jiang Xu
In this work, we study the nonlinear spatially homogeneous Landau equation with hard potential in a close-to-equilibrium framework, we show that the solution to the Cauchy problem…