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荔园学者Colloquium第九十四期

讲座题目: The 3D kinetic Couette flow via the Boltzmann equation in the diffusive limit

主讲人：刘双乾 教授 （华中师范大学）

讲座时间：2024年8月27日下午15：30-16：30

讲座地点：深圳大学粤海校区汇星楼一号教室

内容摘要：In this talk, I will report our recent study on the Boltzmann equation in the diffusive limit in a channel domain $\T^2\times (-1,1)$ for the 3D kinetic Couette flow. Our results demonstrate that the first-order approximation of the solutions is governed by the perturbed incompressible Navier-Stokes-Fourier system around the fluid Couette flow. Moverover, in the absence of external forces, the 3D kinetic Couette flow asymptotically converges over time to the 1D steady planar kinetic Couette flow. Our proof relies on (i) the Fourier transform on $\T^2$ to essentially reduce the 3D problem to a one-dimensional one, (ii) anisotropic Chemin-Lerner type function spaces, incorporating the Wiener algebra, to control nonlinear terms and address the singularity associated with a small Knudsen number in the diffusive limit, and (iii) Caflisch's decomposition, combined with the $L^2\cap L^\infty$ interplay technique, to manage the growth of large velocities. This is a joint work with Renjun Duan, Robert M. Strain and Anita Yang.

主讲人简介：刘双乾，华中师范大学教授。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.等数学刊物上发表论文四十余篇。2023年获国家杰出青年科学基金资助。

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2024年8月21日