Global regularity for a modified critical dissipative quasi-geostrophic equation

Peter Constantin; Gautam Iyer; Wu Jiahong

doi:10.1512/iumj.2008.57.3629

Global regularity for a modified critical dissipative quasi-geostrophic equation

Peter Constantin, Gautam Iyer, Wu Jiahong

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72 Scopus citations

Abstract

In this paper, we consider the modified quasi-geostrophic equation ∂_tθ + (u · ∇)θ + κΛ ^αθ = 0 u = &Lambda^α-1R ^⊥θ, with κ > 0, α ∈ (0, 1] and θ₀ ∈ L²(ℝ²). We remark that the extra Λ^α-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 language	English (US)
Pages (from-to)	2681-2692
Number of pages	12
Journal	Indiana University Mathematics Journal
Volume	57
Issue number	6
DOIs	https://doi.org/10.1512/iumj.2008.57.3629
State	Published - 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Blow up
Global regularity
Nonlocal equations
Quasi-geostrophic equations

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10.1512/iumj.2008.57.3629

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AU - Constantin, Peter

AU - Iyer, Gautam

AU - Jiahong, Wu

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N2 - 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.

AB - 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.

KW - Blow up

KW - Global regularity

KW - Nonlocal equations

KW - Quasi-geostrophic equations

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Global regularity for a modified critical dissipative quasi-geostrophic equation

Abstract

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