Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data

Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data

We seek solutions of the initial value problem for the 2D dissipative quasi-geostrophic (QG) equation with $L^p$ initial data. The 2D dissipative QG equation is a two dimensional model of the 3D incompressible Navier-Stokes equations. We prove global existence and uniqueness of regular solutions for...

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Bibliographic Details
Main Author: Jiahong Wu
Format: Article
Language:English
Published: Texas State University 2001-08-01
Series:Electronic Journal of Differential Equations
Subjects:
2D quasi-geostrophic equation
initial-value problem
existence
uniqueness.
Online Access:http://ejde.math.txstate.edu/Volumes/2001/56/abstr.html
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spelling doaj-9d9fa2646df1401890440a2baf3cfee72020-11-24T22:35:12ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912001-08-01200156113Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> dataJiahong WuWe seek solutions of the initial value problem for the 2D dissipative quasi-geostrophic (QG) equation with $L^p$ initial data. The 2D dissipative QG equation is a two dimensional model of the 3D incompressible Navier-Stokes equations. We prove global existence and uniqueness of regular solutions for the dissipative QG equation with sub-critical powers. For the QG equation with critical or super-critical powers, we establish explicit global $L^p$ bounds for its solutions and conclude that any possible finite time singularity must occur in the first order derivative. http://ejde.math.txstate.edu/Volumes/2001/56/abstr.html2D quasi-geostrophic equationinitial-value problemexistenceuniqueness.
collection DOAJ
language English
format Article
sources DOAJ
author Jiahong Wu
spellingShingle Jiahong Wu
Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
Electronic Journal of Differential Equations
2D quasi-geostrophic equation
initial-value problem
existence
uniqueness.
author_facet Jiahong Wu
author_sort Jiahong Wu
title Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
title_short Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
title_full Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
title_fullStr Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
title_full_unstemmed Dissipative quasi-geostrophic equations with L<small><sup>p</sup></small> data
title_sort dissipative quasi-geostrophic equations with l<small><sup>p</sup></small> data
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2001-08-01
description We seek solutions of the initial value problem for the 2D dissipative quasi-geostrophic (QG) equation with $L^p$ initial data. The 2D dissipative QG equation is a two dimensional model of the 3D incompressible Navier-Stokes equations. We prove global existence and uniqueness of regular solutions for the dissipative QG equation with sub-critical powers. For the QG equation with critical or super-critical powers, we establish explicit global $L^p$ bounds for its solutions and conclude that any possible finite time singularity must occur in the first order derivative.
topic 2D quasi-geostrophic equation
initial-value problem
existence
uniqueness.
url http://ejde.math.txstate.edu/Volumes/2001/56/abstr.html
work_keys_str_mv AT jiahongwu dissipativequasigeostrophicequationswithlsmallsuppsupsmalldata
_version_ 1725724593217339392

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