报告时间：2025年3月15日（星期六）9：00-12：00

报告地点：数学科学学院208会议室

报告及报告人简介：

报告题目：Low regularity Fourier integrators for some nonlinear dispersive equations

报告摘要：In recent years, driven by practical considerations in modeling complex physical systems characterized by rough initial data and non-smooth potentials,there has been growing interest in developing numerical methods capable of handling low regularity scenarios. In this talk, some Fourier integrators are proposed for solving the KdV equation and the nonlinear Schrodinger equation, including the rough initial data and non-smooth potentials. The designation of the scheme is based on the exponential-type integration, Splitting methods andthe Phase-Space analysis of the nonlinear dynamics.

报告人简介：吴奕飞，南京师范大学数学科学学院教授。从事偏微分方程理论和数值计算方面的研究工作，在非线性Schrodinger方程 、KdV方程等整体适定性和低正则算法构造方面做出一系列研究成果，解决了菲尔兹奖获得者T.Tao等提出的长时间遗留问题，设计了目前为止非线性Schrodinger方程和KdV方程正则性要求最低的快速格式，在JEMS、CMP、Adv.Math、Anal.PDE、SINUM、Numer.Math.、Math.Comp.等学术期刊中发表论文。入选国家级领军人才(2023)、青年人才(2019)。

报告题目：Stabilizing effect of the spacetime expansion on the relativistic Euler equations

报告摘要：Recent cosmological evidences show that our universe is undergoing accelerated expansion. The Einstein matter field equations with a positive cosmological constant is one important candidates to explain such phenomenon. Physicists are interested in the nonlinear stability of the background spacetime and the effect of the spacetime expansion on the motion of the matter. In the first part of the talk, I will introduce some results on the global solutions corresponding to the self-gravitating Eulerian fluids (Einstein-Euler equations). In the second part, I introduce the cosmic no hair theorem for the Euler-Poisson system in Newtonian cosmology. Third part focuses on the relation between the expansion rate of the spacetime and the stability of the relativistic Euler equations in fixed spacetime.

报告人简介：魏昌华，浙江理工大学教授。主要从事双曲偏微分方程柯西问题光滑解的整体存在性及奇性形成方面的研究工作。在《Math. Ann.》、 《A. I. H. P. Non Lineaire》、《Cal. Var. PDEs》、 《Ann. Henri Poincare》、 《J. Differential Equations》、《SciChina Math》等学术期刊发表SCI论文20余篇，作为第二完成人获得2019年浙江省自然科学奖二等奖1项。主持国家基金青年及面上项目各1项，浙江省自然科学基金面上项目1项，浙江省自然科学基金杰青项目1项。

报告题目：Wave breaking to the Whitham type equations

报告摘要：We will discuss some wave breaking results to the Whitham type equations. This talk is based on the joint works with J.-C. Saut, S. Sun and Y. Zhang.

报告人简介：王跃循，兰州大学数学与统计学院教授，国家特聘青年专家。曾在挪威科技大学从事博士后研究工作、巴黎萨克雷大学做访问博士后，应邀到挪威、瑞典、加拿大、德国、美国、俄罗斯、法国做学术访问、参加学术会议、作学术报告。主要从事流体力学偏微分方程与色散偏微分方程的研究，相关结果发表在Math. Ann.，ARMA、CPDE、SIMA等国际数学期刊上。

主办单位：数学科学学院

联系人：唐童

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