时间：2020年12月13日

地点：中国科学院数学与系统科学研究院南楼N202

组织者：张志涛，于萌   电话：13260231299

会议简介：杨一米尔斯方程(Yang-Mills equation)是一个重要的微分方程，指杨一米尔斯作用量所确定的欧拉一拉格朗日方程，杨一米尔斯方程也叫做杨—米尔斯理论。杨-米尔斯规范场存在性和质量间隔假设是七大千禧难题之一，为促进这一领域的发展，交流研究进展，我们组织这次Yang-Mills方程研讨会。

 

日程安排：上午8:50-9:00, 开幕式，照相

学术报告：

1.

时间: 上午9:00-10:00

报告人：陈建毅教授 (青岛农业大学)

报告题目: 杨—米尔斯方程适定性问题的研究

摘要： 杨—米尔斯方程的建立是粒子物理发展的一个里程碑，该方程在微分方程理论、粒子物理标准模型的研究中发挥着重要作用。本报告介绍杨—米尔斯方程的物理来源与研究背景，以及在某些规范假设下杨—米尔斯方程解的适定性问题的研究进展。

2.

 时间：上午10:00-11:00

报告人：李奎教授（郑州大学）

报告题目:The threshold theorem for energy critical hyperbolic Yang-Mills equation 摘要：In this talk, I will give an overview of the proof of Oh and Tataru’s Threshold Theorem for the energy criticalhyperbolic Yang-Mills equation. It asserts that the (4+1) dimensional Yang-Mills system is globally well-posed in the caloric gauge for all topologically trivial initial data below twice the ground state energy.

3.

时间：上午11:00-12:00

报告人：罗海军博士（湖南大学）

报告题目: The Yang–Mills heat flow and the caloric gauge

摘要：In this talk, we are first concerned with the study of global solutions for the Yang–Mills heat flow, and establish sharp criteria for global existence and asymptotic convergence to a flat connection for this system.  Our second goal is to use the Yang–Mills heat flow in order to define the caloric gauge. And in this gauge, we can arrive at a good formulation of the hyperbolic Yang–Mills equation, which will play a major role in the proofs of the Threshold Theorem and the Dichotomy Theorem for  the hyperbolic Yang–Mills equation.

午餐、休息：12:00-下午2:30

4.

时间：下午2:30-3:30

报告人：刘海东教授（嘉兴学院）

题目：Existence and multiplicity results for a quasilinear Schrodinger equation

摘要：We consider the quasilinear Schrodinger equation

       

 where V is a potential function and N≥3. Under some natural assumptions on V and h, we prove some existence and multiplicity results. Our method relies on Jeanjean's monotonicity trick, decomposition of bounded Palais-Smale sequence, symmetric mountain pass theorem and Pohozaev identity. This talk is based on joint works with Dr. Yongtao Jing, Prof. Zhaoli Liu and Prof. Leiga Zhao.

5.

时间：下午3:30-4:30

报告人：孙冬冬教授（齐鲁师范大学）

题目：Recent results on Schr？dinger-Kirchhoff equations

摘要：In this talk, we will give a list of results in recent years on Schr？dinger-Kirchhoff equations and we then show our recent results, which contain uniqueness and multiplicity results, results of equations with competing potentials and vanishing potentials, etc.