走向现代数学学术报告 - 陈旭文教授（No. 930)

报告题目：The Well/Ill-posedness Separation of the Boltzmann Equation

报告时间：2026年5月7日 10：00

报告地点：东海岸校区-D209

报 告 人：陈旭文 教授（罗切斯特大学）

邀 请 人：余成杰 教授

报告摘要：We study the well/ill-posedness of the Boltzmann equation with dispersive methods. We construct a family of special solutions, which are neither near equilibrium nor self-similar, and prove the ill-posedness in H^{s} Sobolev space for s<1, despite the fact that the equation is scale invariant at s=1/2. Combining with the previous well-posedness work, we have found that exact well/ill-posedness threshold. This talk is based on a constant collision kernel work, a soft collision kernel work, and a hardsphere collision kernel work.

个人简介：陈旭文，美国罗切斯特大学数学系教授，西蒙斯学者奖获得者，长期获得美国国家科学基金会（NSF）资助。主要从事量子多体问题、动理学方程等领域的偏微分方程的数学理论研究。学术成果发表于 Inventiones Mathematicae, Forum of Mathematics PI, Journal of the European Mathematical Society, Peking Mathematical Journal, Annals of PDE, Archive for Rational Mechanics and Analysis, Communications in Mathematical Physics 等国际顶级期刊。