Mathematical Sciences: Hydrodynamical Scaling Limit of Interacting Particle Systems

丘教授将研究流体流动的欧拉方程在多大程度上可以从哈密顿系统的标度极限中推导出来。最初，这项工作将与一些随机性添加到方程中。该研究项目将与S. Olla和S. rs . Varadhan联合进行。该项目的主要目标是推导出足够长的时间周期的方程，以观察激波，并从微观上理解Lax熵条件。本研究的目的是获得对流体动力学偏微分方程，即欧拉方程的基本理解。从基本观点来看，物质，特别是液体，是由数量巨大但数量有限的粒子（比如原子）组成的，这些粒子相互作用。丘教授的研究项目包括尝试理解如何将流体的通常概念（流体是连续的）与更基本的粒子概念相协调。

Professor Yau will investigate the extent to which the Euler equations of fluid flow can be derived from taking a scaling limit of Hamiltonian systems. Initially this work will be done with some randomness added into the equations. The research project will be carried out jointly with S. Olla and S.R.S. Varadhan. The main goals of the project are to derive the equations for long enough time periods to see shock waves and to understand the Lax entropy conditions microscopically. The aim of this research is to obtain a fundamental understanding of the partial differential equations of fluid dynamics, the Euler equations. From a fundamental point of view, matter, in particular a liquid, is made up of a huge but finite number of particles (say atoms) which are interacting with each other. The research project of Professor Yau involves an attempt to understand how the usual concept of a fluid, which is continuous, can be reconciled with the more fundamental particle concept.