1999 NSF-CBMS Regional Research Conference: Mathematical Analysis of Viscoelastic Flows

粘弹性流体是除了具有粘性和弹性性质外，还具有记忆性的流体。它们在熔融塑料、聚合物溶液、油漆和体液等广泛的技术应用中大量存在。由于其复杂的微观结构，描述这些流体的方程也非常复杂。只有在最近的过去，基本的分析问题的存在，唯一性，和定性行为的解决方案被系统地处理。这些见解中的许多直接促成了数值模拟的成功。虽然这些年来取得了很大的进步，但仍然存在许多挑战。Michael Renardy对粘弹性流体数学建模的研究使他处于这一非常重要学科的前沿。他在国际上享有盛誉，对这一学科有着非常广阔的视野和渊博的知识。作为研究专著“粘弹性数学理论”（1987年）和研究生论文“偏微分方程导论”（1993年）的合著者，以及许多关于粘弹性流动的研究文章，他是唯一有资格对过去二十年来该学科的主要发展进行概述的人，并为跨学科的读者指明了未来的方向。本次会议预计将通过汇集学术界和工业界的成熟研究人员和新来者，激发对粘弹性流体的数学和计算分析研究的兴趣和刺激活动。

Viscoelastic fluids are fluids which in addition to possessing viscous and elastic properties, also have memory. They abound in a wide range of technological applications such as molten plastics, polymer solutions, paints, and body fluids. Due to their complex microstructure, the equations describing these fluids are also very complex. Only in the recent past have fundamental analytical questions of existence, uniqueness, and qualitative behavior of solutions been systematically addressed. Many of these insights havedirectly contributed to successes in numerical simulations. Although great strides have been made during these years many challenges still remain.Michael Renardy's research on the mathematical modeling of viscoelastic fluids places him at the forefront of this very important subject. He has an international reputation and possesses both a very broad viewand profound knowledge of the subject. As a coauthor of the research monograph "Mathematical Theory of Viscoelasticity" (1987) and the graduate text ``An Introduction to Partial Differential Equations'' (1993), as well as numerous research articles on viscoelastic flows, he is uniquely qualified to provide an overview of the major developments in the subject during the past two decades and to indicate directions for the future to an interdisciplinary audience.This conference is expected to stimulate interest and spur activities in research on the mathematical and computational analysis of viscoelastic fluids by bringing together both established researchers and newcomers from academia and industry.