Mathematical Investigation of Nonlinear Free Boundary Problems in Stokes Flow

DMS-9803358首席研究员：S.Tanveer二维和三维斯托克斯流动的数学研究这项建议概述了一类二维和三维慢粘性流体区域自由边界问题的数学研究。继最近关于这类二维非线性自由边界问题的数学结构的显著结果之后，我们试图将该方法推广到三维自由边界问题，并将结果推广到更一般的二维双连通流体区域。在液滴和气泡运动的许多问题中，缓慢的粘性流动是非常自然的。这些在工程应用中都是非常重要的。这一领域的大部分工作都严重依赖于计算机计算；当气泡边界变得复杂时，这种方法就会遇到困难。建议扩展已知的数学技术，以便用铅笔和纸上的结果来补充现有的计算机计算，以便更好地直观地了解至少其中一些问题的精确参数相关性。

DMS-9803358 Principal Investigator: S. Tanveer 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.