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
收藏
页码：53 / 93
页数：41
相关论文
共 50 条
  • [1] Duality approach to regularity problems for the Navier-Stokes equations
    Seregin, Gregory
    TURKISH JOURNAL OF MATHEMATICS, 2023, 47 (03) : 898 - 909
  • [2] Stokes and Navier-Stokes equations with Navier boundary conditions
    Acevedo Tapia, P.
    Amrouche, C.
    Conca, C.
    Ghosh, A.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 285 : 258 - 320
  • [3] FRACTIONAL NAVIER-STOKES EQUATIONS
    Cholewa, Jan W.
    Dlotko, Tomasz
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2018, 23 (08): : 2967 - 2988
  • [4] Convergence of the relaxed compressible Navier-Stokes equations to the incompressible Navier-Stokes equations
    Ju, Qiangchang
    Wang, Zhao
    APPLIED MATHEMATICS LETTERS, 2023, 141
  • [5] Recasting Navier-Stokes equations
    Reddy, M. H. Lakshminarayana
    Dadzie, S. Kokou
    Ocone, Raffaella
    Borg, Matthew K.
    Reese, Jason M.
    JOURNAL OF PHYSICS COMMUNICATIONS, 2019, 3 (10):
  • [6] Euler and Navier-Stokes equations
    Constantin, Peter
    PUBLICACIONS MATEMATIQUES, 2008, 52 (02) : 235 - 265
  • [7] On modifications of the Navier-Stokes equations
    Kobelkov, Georgij M.
    RUSSIAN JOURNAL OF NUMERICAL ANALYSIS AND MATHEMATICAL MODELLING, 2015, 30 (02) : 87 - 93
  • [8] Navier-Stokes equations with delays
    Caraballo, T
    Real, J
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2014): : 2441 - 2453
  • [9] STOCHASTIC NAVIER-STOKES EQUATIONS
    BENSOUSSAN, A
    ACTA APPLICANDAE MATHEMATICAE, 1995, 38 (03) : 267 - 304
  • [10] Stabilization of Navier-Stokes Equations
    Barbu, Viorel
    BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA, 2008, 26 (1-2): : 107 - 116
12345