An Analytical Study of Some Problems in Partial Differential Equations With Applications to Fluid Dynamics and Wave Propagation

Much of the research effort during the grant period was devoted to investigations of periodic waves, and stability in fluid dynamics. Progress was also mad on marching schemes in acoustic wave propagation. In the area of fluid dynamics, problems relating to spiral flows of a viscous incompressible fluid between concentric cylinders in the narrow gap limit were investigated. When the motion of the fluid is driven by rotating and sliding of the cylinders, the problem is that of rotating, plane, Couette flow; when an axial pressure gradient is added, rotating, plane, Couette-Poiseuille flow ensues. Various such problems for viscous, incompressible flow lead to abstract equations in a Banach space B.