Mathematical Sciences: Hydrodynamical Scaling Limit of Interacting Particle Systems

邱教授将研究流体流动的欧拉方程可以在多大程度上通过取哈密顿系统的标度极限来推导。最初，这项工作将在方程中添加一些随机性。该研究项目将与S.Olla和S.R.S.Varadhan联合开展。该项目的主要目标是推导出足够长的时间段的方程，以看到冲击波，并从微观上理解松弛熵条件。这项研究的目的是对流体动力学的偏微分方程组--欧拉方程有一个基本的了解。从根本上讲，物质，尤其是液体，是由数量巨大但数量有限的相互作用的粒子(比如原子)组成的。邱教授的研究项目试图理解如何将通常的连续流体概念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.