摘要：

In this talk, we will discuss recent developments in the regularity theory for the non-cutoff Boltzmann equation on bounded domains, with a specific focus on the Landau and Boltzmann equations. While the classical regularity theory for these kinetic equations has been extensively studied in the context of the whole space and the torus, the analysis becomes significantly more challenging when considering bounded domains, where boundary effects play an essential role. We will present new results on the regularity of solutions to the non-cutoff Boltzmann equation, with a particular emphasis on how the domain boundary influences the behavior of the solution. These insights contribute to a deeper understanding of the impact of boundaries on the dynamics described by the Boltzmann equation and offer new tools for studying kinetic equations in constrained environments.