对偶、矢量平流与Navier-Stokes方程斯托克斯方程
Duality, Vector advection and the Navier-Stokes equations
摘要：
本文证明了三维向量平流方程在下面定义的某种意义下是自对偶的。由此，我们推出了Serrin关于Navier-斯托克斯方程的强解存在性的经典结果.我们还推导了求解矢量平流方程的Feynman-Kac型公式，并指出该公式不是唯一的，即存在不同于标准流动的流动，沿该流动涡量守恒。
英文摘要：
In this article we show that three dimensional vector advection equation is self dual in certain sense defined below. As a consequence, we infer classical result of Serrin of existence of strong solution of Navier-Stokes equation. Also we deduce Feynman-Kac type formula for solution of the vector advection equation and show that the formula is not unique i.e. there exist flows which differ from standard flow along which vorticity is conserved.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
