Solution Properties of a 3D Stochastic Euler Fluid Equation

被引：65

作者：

Crisan, Dan ^{[1
]}

Flandoli, Franco ^{[2
]}

Holm, Darryl D. ^{[1
]}

机构：

[1] Imperial Coll, Dept Math, London SW7 2AZ, England

[2] Univ Pisa, Dept Appl Math, Via Bonanno 25B, I-56126 Pisa, Italy

来源：

JOURNAL OF NONLINEAR SCIENCE | 2019年 / 29卷 / 03期

基金：

英国工程与自然科学研究理事会; 欧洲研究理事会;

关键词：

Analytical properties; Stochastic fluid equations; Lie derivative estimates; MODELS;

D O I：

10.1007/s00332-018-9506-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove local well-posedness in regular spaces and a Beale-Kato-Majda blow-up criterion for a recently derived stochastic model of the 3D Euler fluid equation for incompressible flow. This model describes incompressible fluid motions whose Lagrangian particle paths follow a stochastic process with cylindrical noise and also satisfy Newton's second law in every Lagrangian domain.

引用

页码：813 / 870

页数：58

共 46 条

[1] [Anonymous], 1990, CAMBRIDGE STUDIES AD
[2] [Anonymous], CURRENT PROBLEMS MAT
[3] [Anonymous], 2016, JLAB DATA ANAL PACKA
[4] REMARKS ON THE BREAKDOWN OF SMOOTH SOLUTIONS FOR THE 3-D EULER EQUATIONS
BEALE, JT
KATO, T
MAJDA, A
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1984, 94 (01) : 61 - 66
[5] Brezezniak Z., 1991, Mathematical Models & Methods in Applied Sciences, V1, P41, DOI 10.1142/S0218202591000046
[6] CONSTANTIN P, 1953, DIFFER EQU, V21, P559
[7] A Stochastic Lagrangian representation of the three-dimensional incompressible Navier-Stokes equations
Constantin, Peter
Iyer, Gautam
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2008, 61 (03) : 330 - 345
[8] Cotter, 2018, ARXIV180109729
[9] Cotter C., 2018, ARXIV180205711
[10] Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
Cotter, C. J.
Gottwald, G. A.
Holm, D. D.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2017, 473 (2205):

← 1 2 3 4 5 →