U.S.-Japan Cooperative Research: Hydrodynamic Limit and Non Linear Stochastic Partial Differential Equations

该奖项将支持克利夫兰凯斯西储大学数学和统计系随机和混沌过程科学技术中心Wojbor Woyczynski教授和名古屋大学数学系Tadahisa Funaki教授之间为期两年的美日合作研究项目。目的是在美国和日本的两个中心在水动力极限和非线性随机偏微分方程组领域建立持续、直接的合作。参与该项目的其他研究人员包括凯斯西储大学数学和统计系的Peter Kotelenez教授、东京工业大学应用物理系的内山幸平教授和名古屋大学数学系的长井秀夫教授。研究的目的是在物理相关现象的随机模型领域发展广泛的技术，特别是在物理化学和地球物理流体动力学和海洋学领域，模型的分析、预测和识别将基于统计、机械和概率技术，这些技术考虑相互作用的粒子系统的微观和介观行为，以获得，在热力学或水动力学极限中，由动力学描述的宏观行为往往是非线性偏微分方程式。该项目将把美国和日本科学家开发的不同技术结合在一起，使新技术的开发能够利用这两种方法的最佳部分。

This award will support a two-year U.S.-Japan cooperative research project between Professor Wojbor Woyczynski, Center for Stochastic and Chaotic Processes in Science and Technology, Department of Mathematics and Statistics, Case Western Reserve University, Cleveland, and Professor Tadahisa Funaki, Department of Mathematics, Nagoya University. The purpose is to establish a sustained, direct cooperation in the area of hydrodynamic limits and nonlinear stochastic partial differential equations between the two centers in the United States and Japan. Other investigators involved in the project are Professor Peter Kotelenez, Department of Mathematics and Statistics, Case Western Reserve University, and Professor Kohei Uchiyama, Department of Applied Physics, Tokyo Institute of Technology, and Professor Hideo Nagai, Department of Mathematics, Nagoya University. The objective of the research is to develop a broad spectrum of techniques in the area of stochastic models for physically relevant phenomena, in particular in the areas of physical chemistry and geophysical fluid dynamics and oceanography, The analysis, prediction and identification of the models would be based on statistical, mechanical, and probabilistic techniques that take into account microscopic and mezoscopic behavior of interacting particle systems to obtain, in the thermodynamic or hydrodynamic limits, the macroscopic behavior as described by kinetic often nonlinear partial differential equations. The project will bring together the different techniques developed by the U.S. and Japanese scientists that will permit development of new techniques that utilize the best parts of the two approaches.