广州数学大讲坛第六期

第五十六讲——武汉理工大学曾小雨教授学术报告

题目：Critical Mass Phenomena of Ground States in Stationary Second Order Mean-field Games Systems

时间：2025年10月29日（星期三）上午10:00-12:00

地点：腾讯会议（会议ID:123-746-406）

报告人：曾小雨 教授

摘要：Mean-field games (MFG) systems serve as paradigms to qualitatively describe the game among a huge number of rational players. In this talk, the existence and asymptotic profiles of ground states to MFG systems in the mass critical exponent case are extensively discussed. First of all, we establish the optimal Gagliardo-Nirenberg type inequality associated with the potential-free MFG system. Then, under some mild assumptions on the potential function, we show that there exists a critical mass M* such that the MFG system admits a least energy solution if and only if the total mass of population density M is less than M*. Moreover, the blow-up behavior of energy minimizers are captured as M increases and converges to M*. While studying the existence of least energy solutions, we analyze the maximal regularities of solutions to Hamilton-Jacobi equations with superlinear gradient terms. This is a joint work with Marco Cirant, Fanze Kong and Juncheng Wei.

报告人简介：

曾小雨，教授，博士生导师，武汉理工大学数学与统计学院副院长。国家自然科学基金优秀青年科学基金获得者（2023年）、湖北省“青年拔尖人才”入选者（2022年）。主要研究方向为非线性泛函分析及椭圆型偏微分方程，聚焦于薛定谔方程、玻色-爱因斯坦凝聚中的变分问题，在质量临界约束变分理论、量子多体系统分析等领域取得系统性突破。主持国家自然科学基金项目4项（含优青、面上、青年项目），参与国家自然科学基金重点项目2项。在Trans. Amer. Math. Soc. (TAMS)、J. Funct. Anal. (JFA)、Ann. Inst. H. Poincaré Anal. Non Linéaire、Nonlinearity、J. Differential Equations (JDE)等国际知名期刊发表论文50余篇，研究成果被国际同行广泛引用并引发后续研究。