活动时间：2025-05-30 11:00
活动地点：二号学院楼2432报告厅
主讲人：汪守宏
主讲人中文简介：
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。
活动内容摘要：
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].
主持人：孙春友