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之外还具有记忆性的流体。它们在广泛的技术应用中大量存在，如熔融塑料、聚合物溶液、油漆和体液。 由于其复杂的微观结构，描述这些流体的方程也非常复杂。直到最近，解的存在性、唯一性和定性行为等基本分析问题才得到系统的解决。这些见解中的许多直接促成了数值模拟的成功。 虽然这些年来已经取得了很大的进步，但仍然存在许多挑战。迈克尔·勒纳迪对粘弹性流体数学建模的研究使他处于这一非常重要课题的最前沿。他在国际上享有盛誉，在这方面既有非常广阔的视野，又有渊博的知识。 作为研究专著"粘弹性的数学理论"（1987年）和研究生课本"偏微分方程导论"（1993年）以及关于粘弹性流动的许多研究文章的合著者，他是唯一有资格提供一个概述的主要发展，在过去二十年的主题，并指出方向，为未来的跨学科本次会议预计将通过汇集学术界和工业界的知名研究人员和新人，激发对粘弹性流体的数学和计算分析研究的兴趣并激发活动。

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.