Global regularity for a modified critical dissipative quasi-geostrophic equation

Peter Constantin, Gautam Iyer, Wu Jiahong

Research output: Contribution to journalArticle

54 Scopus citations

Abstract

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇)θ + κΛ αθ = 0 u = &Lambdaα-1R θ, with κ > 0, α ∈ (0, 1] and θ0 ∈ L2(ℝ2). We remark that the extra Λα-1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regularity of strong solutions to this system.

Original languageEnglish (US)
Pages (from-to)2681-2692
Number of pages12
JournalIndiana University Mathematics Journal
Volume57
Issue number6
DOIs
StatePublished - Dec 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Blow up
  • Global regularity
  • Nonlocal equations
  • Quasi-geostrophic equations

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