Mathematical Investigation of Nonlinear Free Boundary Problems in Stokes Flow

主要研究者：S. Tanveer二维和三维Stokes流动的数学研究本论文概述了一类二维和三维缓慢粘性流体区域自由边界问题的数学研究。继最近在二维非线性自由边界问题的数学结构上取得显著成果之后，我们寻求将该方法扩展到三维自由边界问题，并将结果扩展到二维更一般的双连通流体区域。在许多液滴和气泡运动问题中，很自然地会出现缓慢的粘性流动。这些在工程应用中非常重要。这一领域的大部分工作严重依赖于计算机计算；众所周知，当气泡边界变得复杂时，这种方法会遇到困难。建议是扩展已知的数学技术，以便用铅笔和纸上的结果补充现有的计算机计算，从而更好地直观地了解至少其中一些问题的精确参数依赖关系。

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.