学术报告
--- 分析、偏微分方程与动力系统讨论班(2024春季第20、21、22讲)
报告一
On the existence of nontrivial solutions for elliptic equation or system in unbounded domain
赵雷嘎（北京工商大学）
时间：2024年07月06日（周六）下午14:30-15:30
地点：沙河国实E404
摘要: In this talk, we are concerned with a class of elliptic equation or system in unbounded domain. Under suitable assumptions on the nonlinearity, nontrivial solutions and ground states are obtained for the systems via variational methods. In particular, the existence of ground state solution is obtained when the system is indefinite. Normalized solutions are also established for a elliptic equation in unbounded domain.
报告人简介: 赵雷嘎，北京工商大学教授，主要研究非线性泛函分析、临界点理论及其在非线性偏微分方程中的应用等问题。在非线性薛定谔方程以及方程组、Schrödinger-Poisson方程组、哈密尔顿型椭圆方程组、无界区域的椭圆方程边值问题等方面取得了重要的研究成果。 在包括J. Differential Equations、Calc.Var.Partial Differential Equations、Proc. Royal Soc. Edinburgh、Disc.Cont.Dyn.Syst.- A、Commun.Contemp.Math.等重要学术期刊发表30余篇SCI学术论文，受到了国内外同行专家的关注。主持多项国家自然科学基金项目。
报告二
Desingularization of 3D incompressible Euler equations with helical symmetry
万捷（北京理工大学）
时间：2024年07月06日（周六）下午15:30-16:30
地点：沙河国实E404
摘要: In this talk, I will introduce the vortex desingularization problem of 3D incompressible Euler equations. I will discuss some results about the existence and orbital stability of concentrated helical solutions to 3D incompressible Euler equation in infinite pipes, which tend asymptotically to a helix evolved the Binormal Curvature Flow.
报告人简介: 万捷，2020年博士毕业于中科院数学与系统科学研究院应用数学所, 现为北京理工大学数学与统计学院预聘助理教授。主要研究的方向为不可压缩欧拉方程和变分法。
报告三
Uniqueness of vortex patches and vortex helices for the incompressible Euler equations with application to stability
秦国林（北京大学）
时间：2024年07月06日（周六）下午16:30-17:30
地点：沙河国实 E404
摘要: We investigate rigidity properties of concentrated vortices for the incompressible Euler equations by using an approach involving refined estimates of stream functions and linearization of contour dynamics equations. We give completely classification of highly concentrated rotating vortex patches in the unit disk by proving that they must be either a small disk centered at the origin or the unique perturbed small disk rotating around the origin. We also apply our method to establish similar rigidity results for traveling-rotating vortex helices with uniform density near a helical vortex filament for the 3D incompressible Euler equations. As an application of our rigidity results, we further obtain orbital stability of these rotating vortex patches and traveling-rotating vortex helices.
报告人简介: 秦国林，北京大学博士后，主要从事椭圆方程和理想流体方程稳态解的研究。入选2023年博士后创新人才支持计划。在Adv. Math，IMRN, JFA, SIAM, TAMS，CVPDE 等学术期刊发表多篇论文。
邀请人：戴蔚
欢迎大家参加！
