On unbiased stochastic Navier-Stokes equations

被引：20
|
作者：
Mikulevicius, R. [2 ]
Rozovskii, B. L. [1 ]
机构：
[1] Brown Univ, Div Appl Math, Providence, RI 02912 USA
[2] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2012年 / 154卷 / 3-4期
关键词：
Stochastic Navier-Stokes; Unbiased perturbation; Second quantization; Skorokhod integral; Wick product; Kondratiev spaces; Catalan numbers; DRIVEN;
D O I：
10.1007/s00440-011-0384-1
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the original nonlinear term . This perturbation is unbiased in that the expectation of a solution of the perturbed equation solves the deterministic Navier-Stokes equation. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron-Martin version of the Wiener chaos expansion. It is shown that the generalized solution is a Markov process and scales effectively by Catalan numbers.
引用
收藏
页码：787 / 834
页数：48
相关论文
共 50 条
  • [1] On unbiased stochastic Navier–Stokes equations
    R. Mikulevicius
    B. L. Rozovskii
    [J]. Probability Theory and Related Fields, 2012, 154 : 787 - 834
  • [2] STOCHASTIC NAVIER-STOKES EQUATIONS
    CAPINSKI, M
    CUTLAND, N
    [J]. ACTA APPLICANDAE MATHEMATICAE, 1991, 25 (01) : 59 - 85
  • [3] STOCHASTIC NAVIER-STOKES EQUATIONS
    BENSOUSSAN, A
    [J]. ACTA APPLICANDAE MATHEMATICAE, 1995, 38 (03) : 267 - 304
  • [4] NAVIER-STOKES AND STOCHASTIC NAVIER-STOKES EQUATIONS VIA LAGRANGE MULTIPLIERS
    Cruzeiro, Ana Bela
    [J]. JOURNAL OF GEOMETRIC MECHANICS, 2019, 11 (04): : 553 - 560
  • [5] Stochastic cascades and Navier-Stokes equations
    LeJan, Y
    Sznitman, AS
    [J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1997, 324 (07): : 823 - 826
  • [6] Approximations of stochastic Navier-Stokes equations
    Shang, Shijie
    Zhang, Tusheng
    [J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2020, 130 (04) : 2407 - 2432
  • [7] Stochastic Lagrangian Flows and the Navier-Stokes Equations
    Arnaudon, Marc
    Cruzeiro, Ana Bela
    [J]. Stochastic Analysis: A Series of Lectures, 2015, 68 : 55 - 75
  • [8] Partial regularity for the stochastic Navier-Stokes equations
    Flandoli, F
    Romito, M
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (06) : 2207 - 2241
  • [9] STOCHASTIC NAVIER-STOKES EQUATIONS ARE A COUPLED PROBLEM
    Rang, Joachim
    Matthies, Hermann G.
    [J]. COMPUTATIONAL METHODS IN MARINE ENGINEERING V (MARINE 2013), 2013, : 278 - 288
  • [10] Impulse control of stochastic Navier-Stokes equations
    Menaldi, JL
    Sritharan, SS
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (02) : 357 - 381
12345