广州数学大讲坛第三期
第二十一讲——上海交通大学李亚纯教授学术报告
题目:Non-uniqueness in law of Leray solutions to 3D forced stochastic Navier-Stokes equations
时间:2024年4月17日(星期三)下午13:10-15:10
地点:腾讯会议(会议ID:258-622-484)
报告人:李亚纯 教授
摘要:This talk concerns the forced stochastic Navier-Stokes equation driven by additive noise in the three dimensional Euclidean space. By constructing an appropriate forcing term, we prove that there exist distinct Leray solutions in the probabilistically weak sense. In particular, the joint uniqueness in law fails in the Leray class. The non-uniqueness also displays in the probabilistically strong sense in the local time regime, up to stopping times. Furthermore, we discuss the optimality from two different perspectives: sharpness of the hyper-viscous exponent and size of the external force. These results in particular yield that the Lions exponent is the sharp viscosity threshold for the uniqueness/non-uniqueness in law of Leray solutions. This is a joint work with Elia Brué, Rui Jin, and Deng Zhang.
报告人简介:
李亚纯,上海交通大学长聘教授,博士生导师。长期从事非线性偏微分方程的理论与应用研究,先后主持国家级和上海市自然科学基金项目十余项(含国家自然科学基金重点项目1项),发表论文近70篇,出版英文译著3本。国际期刊Comm. Pure Appl. Anal. 和Commun. Math. Anal. Appl. 的编委,上海市曙光学者,入选教育部新世纪优秀人才计划。上海市工业与应用数学学会副理事长,上海市数学建模竞赛组委会副主任,教育部高等学校大学数学课程教学指导委员会委员,高等学校大学数学教学研究与发展中心学术委员会委员。曾获上海市自然科学一等奖和上海市教学成果一等奖,上海市精品课程“工程数学(系列课程)”负责人。