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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Texas State University
2001-08-01
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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 |