报告题目：Global Well-Posedness and Refined Regularity Criterion for the Uni-Directional Euler-Alignment System
报告摘要：We investigate global solutions to the Euler-alignment system in d dimensions with unidirectional flows and strongly singular communication protocols. We obtain global regularity results in both the subcritical regime and the critical regime. Notably, in the critical regime, the system exhibits a critical scaling similar to the critical quasi-geostrophic equation. To achieve global well-posedness, we employ a novel method based on propagating the modulus of continuity. Our approach introduces the concept of simultaneously propagating multiple moduli of continuity, which allows us to effectively handle the system of two equations with critical scaling. Additionally, we improve the regularity criteria for solutions to this system in the supercritical regime. This is a joint work with Qianyun Miao (BIT), Changhui Tan (USC) and Liutang Xue (BNU).
报告时间：2025年5月16日上午10:00
报告地点：数学与统计学院学术报告厅D08
邀 请 人：孙小春 教授 孙晋易 教授
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报告人简介
李亚涛，江西财经大学信息管理与数学学院副教授、硕士生导师。2010年本科毕业于西北师范大学，2020年博士毕业于北京应用物理与计算数学研究所，2022年北京师范大学博士后出站，2024年北京大学数学科学学院访问学者。主要研究方向为流体力学方程的适定性和流动稳定性。主持国家自然科学基金项目1项、江西省科技项目2项，在国际权威期刊 Int. Math. Res. Not.、Indiana Univ.Math.J.、Nonlinearity 等发表SCI学术论文十余篇。
甘肃省数学与统计学基础学科研究中心
数学与统计学院
