Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Michael Dabkowski; Alexander Kiselev; Vlad Vicol

doi:10.1088/0951-7715/25/5/1525

Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Michael Dabkowski, Alexander Kiselev, Vlad Vicol

Mathematics

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

Abstract

We use a non-local maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field u is obtained from the active scalar by a Fourier multiplier with symbol iζ ^⊥|ζ| ^-1m(|ζ|), where m is a smooth increasing function that grows slower than log log|ζ| as |ζ| → ∞.

Original language	English (US)
Pages (from-to)	1525-1535
Number of pages	11
Journal	Nonlinearity
Volume	25
Issue number	5
DOIs	https://doi.org/10.1088/0951-7715/25/5/1525
State	Published - May 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/25/5/1525

Cite this

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abstract = "We use a non-local maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field u is obtained from the active scalar by a Fourier multiplier with symbol iζ ⊥|ζ| -1m(|ζ|), where m is a smooth increasing function that grows slower than log log|ζ| as |ζ| → ∞.",

author = "Michael Dabkowski and Alexander Kiselev and Vlad Vicol",

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AB - We use a non-local maximum principle to prove the global existence of smooth solutions for a slightly supercritical surface quasi-geostrophic equation. By this we mean that the velocity field u is obtained from the active scalar by a Fourier multiplier with symbol iζ ⊥|ζ| -1m(|ζ|), where m is a smooth increasing function that grows slower than log log|ζ| as |ζ| → ∞.

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Global well-posedness for a slightly supercritical surface quasi-geostrophic equation

Abstract

ASJC Scopus subject areas

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