玻尔兹曼方程的梯度流方法

Boltzmann to Landau from the Gradient Flow Perspective

We revisit the grazing collision limit connecting the Boltzmann equation to the Landau(-Fokker-Planck) equation from their recent reinterpretations as gradient flows. Our results are in the same spirit as the $Γ$-convergence of gradient flows technique introduced by Sandier and Serfaty. In this setting, the grazing collision limit reduces to showing the lower semi-continuous convergence of the Boltzmann entropy-dissipation to the Landau entropy-dissipation.

非等温边界玻尔兹曼理论中的梯度衰减

Gradient Decay in the Boltzmann theory of Non-isothermal boundary

研究凸域内非等温漫反射边界下玻尔兹曼方程的解，构造 $W^{1,p}_x$ 解并证明非定常解指数收敛到定常解。

A gradient flow approach to linear Boltzmann equations

We introduce a gradient flow formulation of linear Boltzmann equations. Under a diffusive scaling we derive a diffusion equation by using the machinery of gradient flows.

绕障碍物流动的玻尔兹曼方程的扩散展开

Diffusive Expansion of the Boltzmann equation for the flow past an obstacle

该研究针对流体与动理学方程中的外区域问题，证明含非零来流外区域中玻尔兹曼方程到Navier-Stokes-Fourier系统的扩散展开在临界时间前有效，且将$L^3-L^6$框架应用于无界区域。

强剪切下同能Boltzmann流的非麦克斯韦长期渐近行为

Non Maxwellian long-time asymptotics for Homoenergetic Boltzmann flows under strong shear

利用匹配渐近展开，研究了在双曲主导区域、均匀碰撞核下，含剪切项的非线性Boltzmann方程同能解的长期渐近行为，发现解的质量集中在递增的二进尺度族上，导致与经典麦克斯韦分布截然不同的行为。

空间齐次多原子Boltzmann流的正则性理论

Regularity Theory for the Space Homogeneous Polyatomic Boltzmann Flow

本文研究连续内部能量的多原子Boltzmann方程，针对硬势型碰撞核证明了增益算子平滑效应、导数传播与奇异性指数衰减，并得出解的平滑与粗糙分解定理。