糖心vlog

“七秩工大，学术领航”——70周年校庆系列学术讲座

报告题目：Spectral approach to the Boltzmann equation in a 3D infinite layer

报  告 人：刘双乾

报告时间：2026年6月9日16：30

报告地点：惟德楼315会议室

报告人简介：

刘双乾，华中师范大学糖心vlog 教授、博士生导师、副院长。主要研究基本物理模型的偏微分方程，涉及稀薄气体理论的动理学方程、等离子体的Landau方程、及相关的流体力学方程等领域；在动理学方程的整体适定性、动理学方程的流体动力学极限、以及Boltzmann方程剪切流的稳定性等问题上取得了一系列成果；在Comm. Pure Appl. Math.、 J. Eur. Math. Soc.、 Comm. Math. Phys.、 Arch. Ration. Mech. Anal.、Trans. Amer. Math. Soc.等国际著名数学期刊上发表论文60余篇。2023年获国家杰出青年科学基金资助。

报告简介：

In this talk, I will present a spectral approach to the study of the large-time asymptotic behavior of solutions to the Boltzmann equation near global Maxwellians in a three-dimensional infinite layer $\mathbb{R}^2\times (-1,1)$. The isothermal diffuse reflection boundary condition is imposed on two parallel infinite planes at $x_3=\pm 1$. The main difficulties lie in the fact that the direct Fourier transform is not applicable to the vertical $x_3$-variable, and the linear collision operator $K$ loses its compactness on $L^2((-1,1)\times \R^3_v)$ although it is compact on $L^2(\R^3_v)$. By introducing a regularization operator $K_n$ via the finite-dimensional Fourier series truncation in $L^2(-1,1)$, we study the spectrum of the linearized initial-boundary value approximation problem, establish the resolvent estimates, and identify the leading diffusive eigenvalue. This spectral structure governs the sharp asymptotic dynamics of the original linear problem as $n\to \infty$, enabling us to construct the large-time behavior for the nonlinear problem and rigorously prove that the solution converges with a faster rate toward that of the two-dimensional heat equation in the horizontal direction.

糖心vlog

2026年6月4日