Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation

Liutang Xue; Xiaoxin Zheng

doi:10.1016/j.jde.2012.04.003

Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation

Liutang Xue^*
, Xiaoxin Zheng

^*Corresponding author for this work

China Academy of Engineering Physics

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

16 Scopus citations

Abstract

For the following slightly supercritical surface quasi-geostrophic equation. ∂tθ+u{dot operator}∇;θ+|D|βθ=0,u=∇⊥|D|β-2m(D)θ,β∈]0,1], where m∈C∞(R2\{0}) is a radial non-decreasing positive function which roughly has a logarithmic growth near infinity, we apply the method of nonlocal maximum principle to show the global well-posedness of smooth solutions.

Original language	English
Pages (from-to)	795-813
Number of pages	19
Journal	Journal of Differential Equations
Volume	253
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2012.04.003
State	Published - 15 Jul 2012
Externally published	Yes

Keywords

Modulus of continuity
Nonlocal maximum principle
Slightly supercritical equation
Surface quasi-geostrophic equation

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10.1016/j.jde.2012.04.003

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title = "Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation",

abstract = "For the following slightly supercritical surface quasi-geostrophic equation. ∂tθ+u\{dot operator\}∇;θ+|D|βθ=0,u=∇⊥|D|β-2m(D)θ,β∈]0,1], where m∈C∞(R2\textbackslash{}\{0\}) is a radial non-decreasing positive function which roughly has a logarithmic growth near infinity, we apply the method of nonlocal maximum principle to show the global well-posedness of smooth solutions.",

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author = "Liutang Xue and Xiaoxin Zheng",

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AU - Xue, Liutang

AU - Zheng, Xiaoxin

PY - 2012/7/15

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N2 - For the following slightly supercritical surface quasi-geostrophic equation. ∂tθ+u{dot operator}∇;θ+|D|βθ=0,u=∇⊥|D|β-2m(D)θ,β∈]0,1], where m∈C∞(R2\{0}) is a radial non-decreasing positive function which roughly has a logarithmic growth near infinity, we apply the method of nonlocal maximum principle to show the global well-posedness of smooth solutions.

AB - For the following slightly supercritical surface quasi-geostrophic equation. ∂tθ+u{dot operator}∇;θ+|D|βθ=0,u=∇⊥|D|β-2m(D)θ,β∈]0,1], where m∈C∞(R2\{0}) is a radial non-decreasing positive function which roughly has a logarithmic growth near infinity, we apply the method of nonlocal maximum principle to show the global well-posedness of smooth solutions.

KW - Modulus of continuity

KW - Nonlocal maximum principle

KW - Slightly supercritical equation

KW - Surface quasi-geostrophic equation

UR - https://www.scopus.com/pages/publications/84860610382

U2 - 10.1016/j.jde.2012.04.003

DO - 10.1016/j.jde.2012.04.003

M3 - 文章

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SN - 0022-0396

VL - 253

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EP - 813

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 2

ER -

Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation

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Keywords

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