学术报告论坛报告一: Global solutions of quasi-geostrophic shallow water front problems
报 告 人: 张擎天博士西弗吉尼亚大学
报告时间： 2023年11月30日（星期四）下午14:20-14:55
报告地点： 37号楼3A02报告厅
报告摘要：In this talk, I will introduce the vortex front problem for quasi-geostrophic shallow water equation, which is also known as Hasegawa-Mima equation in plasma science. The contour dynamic equation of the vortex front will be derived, which is a nonlocal, nonlinear dispersive equation. The existence of global solutions will be proved when the initial data is small.
报告人介绍：Dr. Qingtian Zhang graduated from Pennsylvania State University in 2016 with the PhD degree in Applied Math. After that he worked in University of California Davis as a Postdoc. He joined West Virginia University in 2019 as a tenure-track assistant professor. His research interests include analysis of dispersive PDE’s, hyperbolic conservation laws, and fluid mechanics.
论坛报告二: Global dynamics of some spatial three-species food chain models
报 告 人: 武乐云博士香港中文大学
报告时间： 2023年11月30日（星期四）下午14:55-15:30
报告地点： 37号楼3A02报告厅
报告摘要：A food chain is a linearly linked network in a food web starting from producer species and ending at an apex predator species. In this talk, I first introduce how to establish the existence of global classical solutions for some food chain models with various type of taxis by using the structure and energy estimates. Then by constructing Lyapunov functionals, we establish the global stability results under certain conditions.
报告人介绍：武乐云，西北工业大学博士毕业，目前在香港中文大学从事博士后研究。研究方向为偏微分方程。在Adv. Math.，Calc. Var. Partial Differential Equations, SIAM J. Math. Anal.，J. Differential Equations 等杂志发表多篇论文。主持博士后基金面上项目一项，参与重点项目一项。
论坛报告三: Global quasineutral Euler limit for the Vlasov-Poisson-Landau system with rarefaction waves
报 告 人: 杨东成博士香港中文大学
报告时间： 2023年11月30日（星期四）下午15:30-16:05
报告地点： 37号楼3A02报告厅
报告摘要：In this talk, we will consider the Cauchy problem on the spatially one-dimensional Vlasov-Poisson-Landau system modelling the motion of ions under a generalized Boltzmann relation. Let the Knudsen number and the Debye length be given as $\varepsilon>0$ and $\varepsilon^{b}$ with $\frac{3}{5}\leq b\leq 1$, respectively. Under the scaling $(t,x)\to (\varepsilon^{-a}t,\varepsilon^{-a}x)$, for well-prepared initial data we construct the unique global classical solution to the Vlasov-Poisson-Landau system around the rarefaction wave in the vanishing limit $\varepsilon\to 0$ and also obtain the global-in-time convergence of solutions toward the rarefaction wave with rate $\varepsilon^{\frac{3}{5}-\frac{2}{5}a}|\ln\varepsilon|$ in the $L^{\infty}_xL^2_v$ norm. Here $\frac{2}{3}\leq a\leq 1$ if $\frac{2}{3}\leq b\leq 1$ and $4-5b\leq a\leq 1$ if $\frac{3}{5}\leq b< \frac{2}{3}$.
报告人介绍：杨东成，香港中文大学数学系博士后。主要从事非线性偏微分方程，特别是动理学方程及相关的宏观模型的数学理论研究。至今已在“Comm. Math. Phys.”、“Arch. Ration. Mech. Anal.”、“ J. Math. Pures Appl.”、“Math. Models Methods Appl. Sci. ”等知名数学期刊发表论文10余篇。
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数学学院
2023年11月27日