报告题目一: Asymptotic stability on rarefaction wave of one-dimensional Stochastic Burgers equation
报 告 人: 董昭研究员（中国科学院数学与系统科学研究院）
报告时间: 2020年1月4日(周六)，9：30-10：10
报告地点:数学楼2楼学术报告厅
报告摘要：This talk is concerned with the asymptotic behaviour of the solution toward the rarefaction wave for the one dimensional Burgers equation with correlated noise. Under some assumptions of the noise we study the well-posedness of this kind of stochastic PDE. The decay rate of solutions is investigated without integrability of the initial disturbance. The proof is given by energy method with a weight of time. This is joint work with Fei-Min Huang, Hou-Qi Su.
报告人简介: 董昭研究员1996年博士毕业于中科院应用数学研究所。主要从事狄氏型与马氏过程随机过程、随机（偏）微分方程理论研究，特别是在随机流体力学方程和多遍历态的随机动力系统有比较深入的研究。 在国际期刊发表论文50余篇。主持国家自然科学基金委重点项目一项、面上项目两项，参加重点和面上多项，是973项目和基金委创新研究群体的主要成员。和他人合作获得教育部自然科学二等奖。任北京航空航天大学兼职博导，中国科学院大学岗位教授。
报告题目二: Global well-posedness of stochastic nematic liquid crystals with random initial and boundary conditions driven by multiplicative noise
报 告 人: 周国立副教授（重庆大学数学与统计学院）
报告时间: 2020年1月4日(周六)，10：20-11：00
报告地点: 数学楼2楼学术报告厅
报告摘要：The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamical model, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In this article, we consider a $2$-D stochastic nematic liquid crystals with the velocity field perturbed by affine-linear multiplicative white noise, with random initial data and random boundary conditions. Our main objective is to obtain the global well-posedness of the stochastic equations under the sufficient Malliavin regularity of the initial condition. The Malliavin calculus techniques play important roles when we obtain the global existence of the solutions to the stochastic nematic liquid crystal model with random initial and boundary conditions.
报告人简介: 周国立， 重庆大学数学与统计学院副教授。中国科学院和中南大学联合培养, 获博士学位，导师：侯振挺教授，董昭研究员。在北京应用物理与计算数学研究所博士后出站，导师郭柏灵院士。这些年主持了国家面上项目，国家青年项目，国家留学基金委面上项目以及天元基金等，在这些资金的资助下研究了随机流体力学方程的长时间行为和全局适定性，相关结果发表在一些国际期刊：J. Differential Equations, Commun. Math. Sci., Discrete and Continuous Dynamical Systems-B, Nonlinear Analysis TMA, Communications of Pure and Applied Analysis, Computers and Mathematics with Applications, Mathematical Methods in the Applied Sciences, Acta Mathematica Sinica等。
邀请人：程东亚
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