Duality, vector advection and the Navier-Stokes equations

被引：0

作者：

Brzezniak, Z. ^{[1
]}

Neklyudov, M. ^{[1
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

来源：

DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS | 2009年 / 6卷 / 01期

关键词：

Navier-Stokes equations; Feynman Kac formula; vector advection; PROBABILISTIC REPRESENTATION; TRANSPORT-EQUATIONS; UNIQUENESS; FIELDS; FLUID;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：53 / 93

页数：41

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