报告题目：Paracontrolled distribution and stochastic parabolic equations
报 告 人：王玉昭 教授 英国伯明翰大学
报告时间：2025年3月28日，19：00-20：30
报告链接：Join Zoom Meeting ID: 856 3669 3919
https://bham-ac-uk.zoom.us/j/85636693919?pwd=KWBEyFBSGw13jndDvXFMG3aQTsaLJc.1
校内联系人：段犇 bduan@jlu.edu.cn
报告摘要：
In previous lectures, we discussed probabilistic methods for dispersive-type equations, mainly Schrödinger and wave equations, with either random initial data or stochastic forcing. From this lecture, we will move on to discuss stochastic (singular) parabolic-type equations, such as stochastic Navier-Stokes equations and stochastic quantization equations, where renormalization is needed. The main tools here are the paracontrolled distribution argument developed by Gubinelli, etc. The paracontrolled distribution approach is particularly useful for handling singular PDEs by combining techniques from paradifferential calculus (harmonic analysis) and the theory of controlled rough paths.
These arguments can be seen as the parabolic version of the random tensor method that we've discussed. In this lecture, we will start with the (stochastic) incompressible Navier-Stokes equation posed on a two-dimensional torus.
This lecture is based on the following papers:
• G. Da Prato, A. Debussche, J. Funct. Anal. (2002).
• M. Hairer, Invent. Math. (2014).
• M. Gubinelli, P. Imkeller, N. Perkowski, Forum Pi (2015).
• R. Zhu, X. Zhu, JDE (2015).
• J.-C. Mourrat, H. Weber, CMP, (2017).
• R. Catellier, K. Chouk, The Annals of Probability, (2018).
报告人简介：王玉昭，英国伯明翰大学教授，博士生导师。 2005年获吉林大学数学与应用数学学士学位，2010年获北京大学数学博士学位。自2017年8月起在英国伯明翰大学任助理教授，副教授。王玉昭教授主要从事于无穷维动力系统，随机偏微分方程，调和分析的研究 —— 集中于无穷维动力系统的不变测度，随机波动方程的整体适定性相关问题。
