中国科学院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：Prof. Tadahiro Oh (The University of Edinburgh）
题 目：Fourier restriction norm method adapted to controlled paths
时 间：2024.09.27（星期五）13：00-14：00
地 点：思源楼S803
摘 要： Over the last decade, there has been a significant development in the study of stochastic dispersive PDEs, broadly interpreted with random initial data and/or additive stochastic forcing, where the difficulty comes from roughness in spatial regularity. In this talk, I consider well-posedness of stochastic dispersive PDEs with multilpicative noises, whose Ito solutions were constructed in 80's for the wave case and in 90's for the Schrödinger case, and present the first results on pathwise well-posedness for stochastic nonlinear wave equations (SNLW) and stochastic nonlinear Schrödinger equations (SNLS).The main challenge of this problem comes from the deficiency of temporal regularities. We overcome this issue by building a unified framework for controlled rough paths and the Fourier restriction norm method.
