A tamed 3D Navier-Stokes equation in uniform C2-domains

Xicheng Zhang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

In this paper, we analyze a tamed 3D Navier-Stokes equation in uniform C2-domains (not necessarily bounded), which obeys the scaling invariance principle, and prove the existence and uniqueness of strong solutions to this tamed equation. In particular, if there exists a bounded solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, the existence of a global attractor for the tamed equation in bounded domains is also proved. As a simple application, we obtain that the set of all initial values for which the classical Navier-Stokes equation admits a bounded strong solution is open in H2.

Original languageEnglish
Pages (from-to)3093-3112
Number of pages20
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number7-8
DOIs
Publication statusPublished - 1 Oct 2009
Externally publishedYes

Keywords

  • Global attractor
  • Navier-Stokes equation
  • Strong solution

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