流体力学的数学基础（英文）

Mathematical foundations of fluid dynamics

为进一步研究润滑理论,通过流体力学中现有的链式法则,明确给出速度矢量的欧拉形式.利用Stokes′定理的微分形式及一般形式,简化了流体力学的一些结论.特别地,在三维流情况下,讨论了扩展度和环流的概念,并且利用复分析理论,重建了二维流情况下的结果.同时,为便于参考,文中给出复值函数理论和数学分析中的一些结论.

In order to further study the theory of lubrication,by the use of chain rule,the Euler′s form of velocity vectors is achieved.Furthermore,many theoretical results in fluid mechanics are simplified based on the differential forms coupled with the general form of Stokes′theorem.In particular,it elucidates the notion of divergence and circulation in the 3-dimensional flow case,and the results are reestablished in the case of 2-dimensional flow by the use of complex analysis.Finally,for easy reference,some basic results from the theory of complex functions and the results from mathematical analysis are given.