From Boltzmann to Navier–Stokes–Fourier: A Critical Regularity Framework

报告人：李海梁（首都师范大学）

时  间：2026年6月19日9:00

地  点：海韵园行政楼C610

内容摘要:

A fundamental problem in kinetic theory is to connect kinetic descriptions with macroscopic fluid models through hydrodynamic limits. However, a key challenge lies in the mismatch between the critical regularity of the Boltzmann equation and that of the incompressible Navier–Stokes–Fourier system. In this work, we characterize the critical-regularity transition from the Boltzmann equation to the incompressible Navier-Stokes-Fourier system. We prove the global well-posedness of solutions to the Boltzmann equation in a hybrid critical space, uniformly with respect to the Knudsen number \varepsilon. More precisely, we identify a sharp frequency threshold of order 1/\varepsilon separating the low- and high-frequency regimes and show that, as the Knudsen number tends to zero, the low-frequency part of the macroscopic component is governed by the Fujita-Kato critical regularity, whereas the higher-order spatial critical norms of the solution may blow up. In particular, our result admits low-regularity initial data with large-amplitude spatial oscillations. Moreover, we rigorously justify the hydrodynamic limit and establish global-in-time strong convergence with explicit rates for ill-prepared data. This is a joint work with L.-Y. Shou, C.-J. Xu and J. Xu.

个人简介：

李海梁，首都师范大学教授、博导，国家杰出青年科学基金获得者，入选“北京学者”计划，享受国务院政府特殊津贴。主要研究领域为偏微分方程的数学理论, 在Comm. Math. Phys., Arch. Ration. Mech. Anal., SIAM J. Math. Anal.等国际重要期刊发表论文100多篇。现任中国工业与应用数学学会常务理事、首都师范大学科协常务副主席。

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