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

Igor Kukavica, Vlad Vicol

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)189-206
Number of pages18
JournalAsymptotic Analysis
Volume90
Issue number3-4
DOIs
StatePublished - Jan 1 2014

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Stochastic Navier-Stokes Equation
Strong Solution
Bounded Domain
Moment
Long-time Behavior
Statistical property
Navier-Stokes Equations
Differential equation

Keywords

  • moments
  • pathwise solutions
  • stochastic Navier-Stokes equations

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain. / Kukavica, Igor; Vicol, Vlad.

In: Asymptotic Analysis, Vol. 90, No. 3-4, 01.01.2014, p. 189-206.

Research output: Contribution to journalArticle

Kukavica, Igor ; Vicol, Vlad. / Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain. In: Asymptotic Analysis. 2014 ; Vol. 90, No. 3-4. pp. 189-206.
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