应兰州大学数学与统计学院邀请，美国印第安纳大学数学系汪守宏教授将于2025年5月11—31日访问我校并作学术报告，欢迎全校师生参加。
报告题目：Dynamical Transitions in Fluid Flows
报告时间：2025年5月12日上午10:00
报告地点：理工楼631
报告摘要：The first part of the talk is to introduce the general framework of phase transition dynamics for deterministic dissipative systems, with various applications to statistical physics and fluid flows. This is based on joint work with Dr. Tian Ma. In the second part, we study transitions in stochastic non-equilibrium systems. As we know, a central challenge in physics is to describe non-equilibrium systems driven by randomness. For deterministic systems, the center manifold theory has shown a prodigious efficiency to often completely characterize how the onset of linear instability translates into the emergence of nonlinear patterns, associated with genuine physical regimes. In presence of random fluctuations, the underlying reduction principle to the center manifold is seriously challenged due to large excursions caused by the noise. We present an alternative framework to cope with these difficulties exploiting the approximation theory of stochastic invariant manifolds, on one hand, and energy estimates measuring the defect of parameterization of the high-modes, on the other. As a result, the approach enables us to predict, from reduced equations of the stochastic fluid problem, the occurrence in large probability of a stochastic analogue to the pitchfork bifurcation. This is joint work with Mickael Chekroun, Honghu Liu, and James McWilliams [JDE, 346(2023), 145-204].
报告人简介
汪守宏，美国印第安纳大学数学系教授。长期致力于非线性偏微分方程、流体力学、大气动力学和理论物理的交叉研究，在Navier-Stokes方程的边界层理论和统计解等方面有诸多成果。与J. Nirenberg院士、J. Lions院士、R. Temam院士、丑纪范院士等国际顶尖学者保持长期深度合作，在《Journal of Mathematical Fluid Mechanics》《SIAM Journal on Applied Mathematics》等期刊发表论文100余篇，被引逾4000次。出版《Phase Transition Dynamics》《Mathematical Principles of Theoretical Physics》等8部专著，部分著作被列为应用数学研究生教材。曾任Discrete and Continuous Dynamical Systems - B编委。多次受邀在SIAM应用数学年会、国际工业与应用数学大会（ICIAM）等权威学术会议作特邀报告，并积极参与国际合作研究，培养了一批优秀的博士生和青年学者。
数学与统计学院
甘肃应用数学中心
萃英学院
2025年05月10日
