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.
