学术报告（寿凌云 2025.10.30）

摘要：A fundamental challenge in the study of the Boltzmann equation is to identify the minimal regularity space that ensures global well-posedness of solutions. This work addresses the Cauchy problem for the angularly cutoff, three-dimensional Boltzmann equation. We establish the existence of a unique global solution for initial data near a global Maxwellian in a spatially critical homogeneous hybrid Besov space. Furthermore, we prove that both the solution and its highest derivatives converge to equilibrium at optimal decay rates, provided that the initial perturbation lies in a lower-regularity Besov space.  Our proof relies on the construction of spectrally localized Lyapunov functionals via hypocoercivity, capturing sharp dissipation mechanisms across both low- and high-frequency regimes. As an application, we further demonstrate how this functional setting can be employed to justify the hydrodynamic limit toward the Navier-Stokes-Fourier system.