京都大学でスペクトル・散乱理論に関するセミナーを行っています。
日時 2025 年 12 月 12 日（金）午後3時30分--午後5時00分 December 12th (Fri.), 2025, P.M. 3:30--P.M. 5:00 講演形式 対面式 場所 京都大学人間・環境学研究科棟 2階226号室 講演者 波多間 備（京都大学 数理解析研究所 学振PD） 講演題目 Uniform dispersive estimates for the semi-classical Hartree equation with long-range interaction 講演要旨 In this talk, we consider the Hartree equation with smooth but long-range interaction in the semiclassical regime, in three-dimensional space. We show that the density function of small-data solution decays at the optimal rate. When the semi-classical parameter $\hbar\in(0,1]$ is fixed, our result is essentially covered by the recent work by Nguyen and You; however, the novelty is the uniformity with respect to $\hbar$. Namely, both smallness conditions for initial data and bounds for the solution are independent of $\hbar$.