Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain

Igor Kukavica; Vlad Vicol

doi:10.3233/ASY-141237

Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain

Igor Kukavica, Vlad Vicol

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We address a question posed by Glatt-Holtz and Ziane in Advances in Differential Equations 14 (2009), 567-600, regarding moments of strong pathwise solutions to the Navier-Stokes equations in a two-dimensional bounded domain. We prove that Eφ(u(t)H¹()²)<∞ for any deterministic t>0, where φ(x)=log(1+log(1+x)). Such moment bounds may be used to study statistical properties of the long time behavior of the equation. In addition, we obtain algebraic moment bounds on compact subdomains ₀ of the form Eφ_O(u(t)H¹(₀)²)<, where φ_O(x)=(1+x)¹², for any deterministic t>0 and any ε>0.

Original language	English (US)
Pages (from-to)	189-206
Number of pages	18
Journal	Asymptotic Analysis
Volume	90
Issue number	3-4
DOIs	https://doi.org/10.3233/ASY-141237
State	Published - 2014

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

moments
pathwise solutions
stochastic Navier-Stokes equations

Access to Document

10.3233/ASY-141237

Cite this

@article{8fd02581afc346f8949f8bb7c6c34156,

title = "Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain",

abstract = "We address a question posed by Glatt-Holtz and Ziane in Advances in Differential Equations 14 (2009), 567-600, regarding moments of strong pathwise solutions to the Navier-Stokes equations in a two-dimensional bounded domain. We prove that Eφ(u(t)H1()2)<∞ for any deterministic t>0, where φ(x)=log(1+log(1+x)). Such moment bounds may be used to study statistical properties of the long time behavior of the equation. In addition, we obtain algebraic moment bounds on compact subdomains 0 of the form EφO(u(t)H1(0)2)<, where φO(x)=(1+x)12, for any deterministic t>0 and any ε>0.",

keywords = "moments, pathwise solutions, stochastic Navier-Stokes equations",

author = "Igor Kukavica and Vlad Vicol",

year = "2014",

doi = "10.3233/ASY-141237",

language = "English (US)",

volume = "90",

pages = "189--206",

journal = "Asymptotic Analysis",

issn = "0921-7134",

publisher = "SAGE Publications Ltd",

number = "3-4",

}

TY - JOUR

T1 - Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain

AU - Kukavica, Igor

AU - Vicol, Vlad

PY - 2014

Y1 - 2014

N2 - We address a question posed by Glatt-Holtz and Ziane in Advances in Differential Equations 14 (2009), 567-600, regarding moments of strong pathwise solutions to the Navier-Stokes equations in a two-dimensional bounded domain. We prove that Eφ(u(t)H1()2)<∞ for any deterministic t>0, where φ(x)=log(1+log(1+x)). Such moment bounds may be used to study statistical properties of the long time behavior of the equation. In addition, we obtain algebraic moment bounds on compact subdomains 0 of the form EφO(u(t)H1(0)2)<, where φO(x)=(1+x)12, for any deterministic t>0 and any ε>0.

AB - We address a question posed by Glatt-Holtz and Ziane in Advances in Differential Equations 14 (2009), 567-600, regarding moments of strong pathwise solutions to the Navier-Stokes equations in a two-dimensional bounded domain. We prove that Eφ(u(t)H1()2)<∞ for any deterministic t>0, where φ(x)=log(1+log(1+x)). Such moment bounds may be used to study statistical properties of the long time behavior of the equation. In addition, we obtain algebraic moment bounds on compact subdomains 0 of the form EφO(u(t)H1(0)2)<, where φO(x)=(1+x)12, for any deterministic t>0 and any ε>0.

KW - moments

KW - pathwise solutions

KW - stochastic Navier-Stokes equations

UR - https://www.scopus.com/pages/publications/84911920953

UR - https://www.scopus.com/inward/citedby.url?scp=84911920953&partnerID=8YFLogxK

U2 - 10.3233/ASY-141237

DO - 10.3233/ASY-141237

M3 - Article

AN - SCOPUS:84911920953

SN - 0921-7134

VL - 90

SP - 189

EP - 206

JO - Asymptotic Analysis

JF - Asymptotic Analysis

IS - 3-4

ER -

Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this