Inviscid limits for a stochastically forced shell model of turbulent flow

被引：15

作者：

Friedlander, Susan ^{[1
]}

Glatt-Holtz, Nathan ^{[2
]}

Vicol, Vlad ^{[3
]}

机构：

[1] Univ Southern Calif, Los Angeles, CA 90089 USA

[2] Virginia Tech, Blacksburg, VA 24061 USA

[3] Princeton Univ, Princeton, NJ 08544 USA

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 03期

基金：

美国国家科学基金会;

关键词：

Inviscid limits; Invariant measures; Dissipation anomaly; Shell models; Ergodicity; NAVIER-STOKES EQUATIONS; ANOMALOUS DISSIPATION; ENERGY-CONSERVATION; EULER; ERGODICITY; CONJECTURE; ONSAGER;

D O I：

10.1214/14-AIHP663

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：

We establish the anomalous mean dissipation rate of energy in the inviscid limit for a stochastic shell model of turbulent fluid flow. The proof relies on viscosity independent bounds for stationary solutions and on establishing ergodic and mixing properties for the viscous model. The shell model is subject to a degenerate stochastic forcing in the sense that noise acts directly only through one wavenumber. We show that it is hypo-elliptic (in the sense of Hormander) and use this property to prove a gradient bound on the Markov semigroup.

引用

页码：1217 / 1247

页数：31

共 59 条

[1]

Albeverio S., 2008, LECT NOTES MATH, V1942

[2]

[Anonymous], 1992, ENCY MATH ITS APPL, DOI DOI 10.1017/CBO9780511666223

[3] UNIQUENESS FOR A STOCHASTIC INVISCID DYADIC MODEL [J].