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

報 告 人： 曾小雨

時    間：2024年6月27日上午11：00--12：00

地   點：騰訊會議（會議号：143545359）

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, some intricate connections between MFGs and Schrodinger equations are mentioned, then 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*. In particular, given the precise asymptotic expansions of the potential, we establish the refined blow-up behavior of ground states. 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.

報告人簡介：

曾小雨，男，理學博士，武漢理工大學數學科學中心教授，2009年本科畢業于華中師範大學，2014年博士畢業于中科院武漢物理與數學研究所。研究方向為非線性泛函分析與橢圓型偏微分方程，在玻色-愛因斯坦凝聚相關變分問題以及抛物方程爆破解構造方面取得系列進展。主要成果發表在Trans.AMS、JFA、Ann. Inst. H. Poincar'eAnal. Non Lin'eaire、Nolinearity等國際期刊上。主持國家自然科學基金3項，作為核心成員參與國家自然科學基金重點項目。