报告题目：Stochastic strong solutions for stochastic transport equations  

报告人：高洪俊  教授   南京师范大学

报告摘要：We investigate a stochastic transport equation driven by a multiplicative noise. For drift coefficients in $L^q(0,T;{ \mathcal C}^\alpha_b({ \mathbb R}^d))$ ($\alpha>2/q$) and initial data in$W^{1,r}({ \mathbb R}^d)$, we show the existence and uniqueness of stochastic strong solutions. Opposite to the deterministic case where the same assumptions on drift coefficients and initial data may induce nonexistence of strong solutions, we prove that a multiplicative stochastic perturbation of Brownian type is enough to render the equation well-posed. However, for $\alpha+1<2/q$ with spatial dimension higher than one, we can choose proper initial data and drift coefficients so that the stochastic strong solutions do not exist. Moreover, if the drift coefficients belong to $L^q(0,T;W^{1,p}({ \mathbb R}^d))$, we also derive the global integrability for stochastic strong solutions. This responds to the question raised by Fedrizzi and Flandoli in the case of drift coefficients in $L^q(0,T;L^p({ \mathbb R}^d))$, and we thus partially extend their earlier results.

报告时间：2018年5月2日（周三）下午2:30-3:30

报告地点：威廉希尔中文网站三楼专家接待室

报告人简介：南京师范大学教授、博士生导师，科技处处长。美国数学评论评论员，Stochastics and Dynamics（SCI）编委,南京师范大学自然科学版副主编,江苏省工业与应用数学学会副理事长,江苏省高校“大规模复杂系统数值模拟”重点实验室副主任，江苏省“青蓝工程”中青年学术带头人，江苏省“333”工程第三层次培养人选，国防科工委科技进步奖一等奖获得者（排名第二）.目前研究兴趣为非线性发展方程和无穷维动力系统，物理、力学和地球科学(Geoscience)中的随机偏微分方程和无穷维随机动力学。目前已发表包括Adv. Math.、SIAM J. Math. Anal.、J.Differential Equations和中国科学在内的国内外重要期刊论文160多篇。多次主持国家基金项目，参与973项目，目前主持国家自然科学基金重点项目，主持江苏省自然科学基一项，主持江苏省青蓝工程科研基金一项。