A Mathematical Investigation of 2-D and 3-D Stokes flow
This proposal outlines a mathematical investigation of a class of free boundary problems for slow viscous fluid regions in both two and three dimensions. Following recent remarkable results on the mathematical structure of such nonlinear free boundary problems in 2-D, we seek to extend the methodology to free boundary problems in three dimensions, as well as extend the results to more general doubly connected fluid regions in two dimensions.
Slow viscous flows arise very naturally in many problems of drops and bubble motion. These are very important in engineering applications. Most of the work in this area relies heavily on computer calculation; for cases when the bubble boundary becomes complicated, such methods are known to run into difficulties. The proposal is to extend the known mathematical techniques so as to complement existing computer calculations with pencil and paper results that gives better intuition on the precise parameter dependences in at least a few of these problems.
