Behavior of solutions of 2D quasi-geostrophic equations

Peter Constantin; Jiahong Wu

doi:10.1137/S0036141098337333

Behavior of solutions of 2D quasi-geostrophic equations

Peter Constantin, Jiahong Wu

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

315 Scopus citations

Abstract

We study solutions to the 2D quasi-geostrophic (QGS) equation ∂θ/∂t + u · ▽θ + κ(-△)^αθ = f and prove global existence and uniqueness of smooth solutions if α ∈ (1/2, 1]; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.

Original language	English (US)
Pages (from-to)	937-948
Number of pages	12
Journal	SIAM Journal on Mathematical Analysis
Volume	30
Issue number	5
DOIs	https://doi.org/10.1137/S0036141098337333
State	Published - 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computational Mathematics
Analysis
Applied Mathematics

Keywords

Existence
Large time approximation
Quasi-geostrophic equation
Uniqueness

Access to Document

10.1137/S0036141098337333

Cite this

@article{18118e582a424b8e9afca1cf2b86a955,

title = "Behavior of solutions of 2D quasi-geostrophic equations",

abstract = "We study solutions to the 2D quasi-geostrophic (QGS) equation ∂θ/∂t + u · ▽θ + κ(-△)αθ = f and prove global existence and uniqueness of smooth solutions if α ∈ (1/2, 1]; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.",

keywords = "Existence, Large time approximation, Quasi-geostrophic equation, Uniqueness",

author = "Peter Constantin and Jiahong Wu",

year = "1999",

doi = "10.1137/S0036141098337333",

language = "English (US)",

volume = "30",

pages = "937--948",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "5",

}

TY - JOUR

T1 - Behavior of solutions of 2D quasi-geostrophic equations

AU - Constantin, Peter

AU - Wu, Jiahong

PY - 1999

Y1 - 1999

N2 - We study solutions to the 2D quasi-geostrophic (QGS) equation ∂θ/∂t + u · ▽θ + κ(-△)αθ = f and prove global existence and uniqueness of smooth solutions if α ∈ (1/2, 1]; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.

AB - We study solutions to the 2D quasi-geostrophic (QGS) equation ∂θ/∂t + u · ▽θ + κ(-△)αθ = f and prove global existence and uniqueness of smooth solutions if α ∈ (1/2, 1]; weak solutions also exist globally but are proven to be unique only in the class of strong solutions. Detailed aspects of large time approximation by the linear QGS equation are obtained.

KW - Existence

KW - Large time approximation

KW - Quasi-geostrophic equation

KW - Uniqueness

UR - http://www.scopus.com/inward/record.url?scp=0033419179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033419179&partnerID=8YFLogxK

U2 - 10.1137/S0036141098337333

DO - 10.1137/S0036141098337333

M3 - Article

AN - SCOPUS:0033419179

SN - 0036-1410

VL - 30

SP - 937

EP - 948

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 5

ER -

Behavior of solutions of 2D quasi-geostrophic equations

Abstract

All Science Journal Classification (ASJC) codes

Keywords

Access to Document

Other files and links

Fingerprint

Cite this