報告人：張明波 副教授
報告題目：Noise Regularization for Jump-Type Transport Equations with Singular Coefficients
報告時間：2026年5月16日（周六）上午9：00
報告地點：云龍校區6號樓304報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
張明波：江西財經大學統計與數據科學學院，博士畢業于中山大學數學學院，研究方向隨機微分方程。
報告摘要：
We consider a stochastic transport equation with a jump term and investigate the no-blow-up problem. The drift coefficient is assumed only to be integrable. Unlike the deterministic case, where smooth initial conditions may give rise to discontinuities, we show that a certain level of Sobolev regularity is preserved, which in turn implies H\{o}lder continuity of the solutions. To establish the existence, uniqueness, and regularity of solutions for this equation, we study a more general fully nonlinear stochastic partial differential equation with jumps via the method of characteristics. The proof of the maintained regularity is rigorously established through a detailed analysis of the associated stochastic flow of characteristics.