Mathematical Sciences: Mathematical Problems in Continuum Mechanics

有了这个奖项，主要研究人员将研究 连续统数学理论中的各种问题 力学 尤其是，他们将调查井- 某些边值问题的适定性描述了 粘弹性流体的流动和 牛顿流体，如水。 这些都是难题 涉及"开放"的流入和流出边界， 的边界条件确定适定性的 问题. 边界类型的精确确定 导致适定问题的条件是一个主要的 研究的目标。 自然界中许多流体的行为通常是直接的 流体状态和作用于其上的力的结果 沿着流动状态的边界。 这些所谓的边界 条件可以是许多不同的类型，但只有 物理上相关的是科学家感兴趣的， 数学家 在数学上， 边界条件是一个导致唯一的解决方案， 微分方程的基本系统。 有了这个奖项， 研究人员将研究哪些类型的物理相关边界 条件是可能的，在各种流动的普通流体， 水和更复杂的粘弹性流体。

With this award the principal investigators will study various problems in the mathematical theory of continuum mechanics. In particular, they will investigate the well- posedness of certain boundary value problems that describe the flows of visco-elastic fluids and the free-surface flows of Newtonian fluids such as water. These are difficult problems that involve "open" inflow and outflow boundaries, and the nature of the boundary conditions determine the well-posedness of the problem. A precise determination of the types of boundary conditions that lead to well-posed problems is one of the major goals of the research. The behavior of many fluids in nature is very often a direct result of the state of the fluid and the forces acting upon it along the boundary of the flow regime. These so-called boundary conditions can be of many different types, but only the physically relevant ones are of interest to scientists and mathematicians. In a mathematical context a physically relevant boundary condition is one that leads to a unique solution of the underlying system of differential equations. With this award the researchers will study what types of physically relevant boundary conditions are possible in various flows of ordinary fluids like water and more complicated visco-elastic fluids.