Mathematical Sciences: Mathematical Problems in Continuum Mechanics

有了这个奖，主要研究人员将研究连续介质力学数学理论中的各种问题。特别是，他们将研究描述粘弹性流体流动和牛顿流体(如水)自由表面流动的某些边值问题的适定性。这些都是涉及“开放”流入和流出边界的难题，而边界条件的性质决定了问题的适定性。精确地确定导致适定问题的边界条件的类型是研究的主要目标之一。自然界中许多流体的行为往往是流体状态和沿流动状态边界作用于其上的力的直接结果。这些所谓的边界条件可以有许多不同的类型，但只有物理上相关的条件才是科学家和数学家感兴趣的。在数学背景下，物理上相关的边界条件是导致基本微分方程组的唯一解的条件。有了这一奖项，研究人员将研究在水等普通流体和更复杂的粘弹性流体的各种流动中可能存在的物理相关的边界条件。

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.