Mathematical Investigation of Nonlinear Free Boundary Problems in Stokes Flow

DMS-9803358主要研究者：S. Tanveer 2-D和3-D Stokes流的数学研究该提案概述了对二维和三维缓慢粘性流体区域的一类自由边界问题的数学研究。最近显着的成果，这种非线性自由边界问题的数学结构在2-D，我们试图将该方法扩展到自由边界问题的三维空间，以及扩展到更一般的双连通流体区域的结果在两个维度。在许多液滴和气泡运动的问题中，很自然地会出现慢粘性流动.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;对于气泡边界变得复杂的情况，已知这种方法会遇到困难。该建议是扩展已知的数学技术，以补充现有的计算机计算与铅笔和纸张的结果，使更好的直观的精确的参数依赖性，至少在一些这些问题。

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.