Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

Peter Constantin; Jiahong Wu

doi:10.1016/j.anihpc.2007.10.001

Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

Peter Constantin, Jiahong Wu

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

100 Scopus citations

Abstract

We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1 / 2) dissipation (- Δ)^α: If a Leray-Hopf weak solution is Hölder continuous θ ∈ C^δ (R²) with δ > 1 - 2 α on the time interval [t₀, t], then it is actually a classical solution on (t₀, t].

Original language	English (US)
Pages (from-to)	1103-1110
Number of pages	8
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	25
Issue number	6
DOIs	https://doi.org/10.1016/j.anihpc.2007.10.001
State	Published - 2008
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematical Physics
Applied Mathematics

Keywords

2D quasi-geostrophic equation
Regularity
Supercritical dissipation
Weak solutions

Access to Document

10.1016/j.anihpc.2007.10.001

Cite this

@article{3b8bdf3ad41f474a958fc7f7618657ce,

title = "Regularity of H{\"o}lder continuous solutions of the supercritical quasi-geostrophic equation",

abstract = "We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1 / 2) dissipation (- Δ)α: If a Leray-Hopf weak solution is H{\"o}lder continuous θ ∈ Cδ (R2) with δ > 1 - 2 α on the time interval [t0, t], then it is actually a classical solution on (t0, t].",

keywords = "2D quasi-geostrophic equation, Regularity, Supercritical dissipation, Weak solutions",

author = "Peter Constantin and Jiahong Wu",

note = "Funding Information: PC was partially supported by NSF-DMS 0504213. JW thanks the Department of Mathematics at the University of Chicago for its support and hospitality.",

year = "2008",

doi = "10.1016/j.anihpc.2007.10.001",

language = "English (US)",

volume = "25",

pages = "1103--1110",

journal = "Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire",

issn = "0294-1449",

publisher = "Elsevier Masson SAS",

number = "6",

}

TY - JOUR

T1 - Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

AU - Constantin, Peter

AU - Wu, Jiahong

N1 - Funding Information: PC was partially supported by NSF-DMS 0504213. JW thanks the Department of Mathematics at the University of Chicago for its support and hospitality.

PY - 2008

Y1 - 2008

N2 - We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1 / 2) dissipation (- Δ)α: If a Leray-Hopf weak solution is Hölder continuous θ ∈ Cδ (R2) with δ > 1 - 2 α on the time interval [t0, t], then it is actually a classical solution on (t0, t].

AB - We present a regularity result for weak solutions of the 2D quasi-geostrophic equation with supercritical (α < 1 / 2) dissipation (- Δ)α: If a Leray-Hopf weak solution is Hölder continuous θ ∈ Cδ (R2) with δ > 1 - 2 α on the time interval [t0, t], then it is actually a classical solution on (t0, t].

KW - 2D quasi-geostrophic equation

KW - Regularity

KW - Supercritical dissipation

KW - Weak solutions

UR - http://www.scopus.com/inward/record.url?scp=54549116855&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=54549116855&partnerID=8YFLogxK

U2 - 10.1016/j.anihpc.2007.10.001

DO - 10.1016/j.anihpc.2007.10.001

M3 - Article

AN - SCOPUS:54549116855

SN - 0294-1449

VL - 25

SP - 1103

EP - 1110

JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire

IS - 6

ER -

Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this