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.
