报告题目1: Sharp  blow-up result for the intercritical   Inhomogeneous  NLS equation

报告人：李渊， 华中师范大学

报告时间：2023年7月2日14：00-15：30

报告地点：20-417

报告摘要：In this talk, we consider the intercritical inhomogeneous nonlinear Schr\odinger equation. For the radial symmetry initial data,   we construct the ring blow-up solutions and obtain blow-up speed. This result implies that the upper bound on the blow-up speed given by Cardoso and Farah [J. Funct. Anal.,281(8) No. 109134, (2021)] is sharp.

报告人简介：李渊，现在华中师范大学数学博士后流动站工作，合作导师为彭双阶教授。2021年6月博士毕业于兰州大学。2019年至2021年在意大利比萨大学联合培养，主要从事薛定谔方程以及半波方程的爆破解以及爆破速率等方面的研究。在Comm. Partial Differential Equations, J. Funct. Anal.,等杂志上发表论文多篇。主持中国博士后科学基金面上资助和湖北省博士后创新项目。

报告题目2: Structural Stability of Transonic Shock Flows with External Forcing

报告人：杨文刚，武汉大学

报告时间：2023年7月2日15：30-17：00

报告地点：20-417

报告摘要：In this talk, we are concerned with the structural stability of a one-dimensional transonic shock with external force passing through a two-dimensional flat nozzle. We first establish the existence and uniqueness of one-dimensional transonic shock solutions to steady Euler system with external force by prescribing suitable pressure at the exit of the nozzle when the upstream flow is a uniform supersonic flow. Then we investigate the structural stability of these transonic shock solutions in two-dimensional flat nozzle when the exit pressure is suitably perturbed. One of new ingredients in our analysis is to use the deformation-curl decomposition developed in [27] to steady Euler system to deal with the transonic shock problem. It is shown that the external force helps to stabilize the transonic shock in flat nozzles and the shock position is uniquely determined.

报告人简介：杨文刚，2023年6月博士毕业于武汉大学，2023年7月将在武汉大学数学博士后流动站工作，主要研究理想气体跨音速激波的稳定性问题，在J. Evol. Equ.，Appl. Anal.等国际期刊上发表文章多篇。

邀请人：非线性分析与PDE团队