Global Well-posedness for 2D Generalized Parabolic Anderson Model via Paracontrolled Calculus
报告专家：朱湘禅研究员（中国科学院数学与系统科学研究院）
报告时间：2024年3月29日下午14:30-15:30
报告地点：腾讯会议：594-527-066 会议密码：0329
报告摘要：In this talk we revisits the problem of global well-posedness for the generalized parabolic Anderson model on R + ×T 2 within the framework of paracontrolled calculus [GIP15]. The model is given by the equation: (∂t − ∆)u = F (u)η where η ∈ C −1−κ with 1/6 > κ > 0, and F ∈ C 2 b (R). Assume that η ∈ C −1−κ and can be lifted to enhanced noise, we derive new a priori bounds. The key idea follows from the recent work [CFW24] by A.Chandra, G.L. Feltes and H.Weber to represent the leading error term as a transport type term, and our techniques encompass the paracontrolled calculus, the maximum principle, and the localization approach (i.e. high-low frequency argument).
专家简介：朱湘禅，中国科学院数学与系统科学研究院应用数学研究所研究员，2012年于北京大学和德国比勒菲尔德大学获得博士学位。主要研究方向是随机分析和随机偏微分方程，具体包括奇异随机偏微分方程和随机流体方程等。在Comm. Pure Appl. Math.，Comm. Math. Phys.， Ann. Probab.， Probab. Theory Related Fields, J. Funct. Anal. 等期刊上发表了多篇论文。
邀请人：胡泽春
