Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity

In this article, the author studies the regularity of 3D generalized Navier-Stokes (GNS) equations with fractional dissipative terms $(-Delta)^{alpha} u$. It is proved that if $hbox{div} (u / |u|) in L^p (0, T ; L^q (mathbb{R}^3))$ with $$ frac{2 alpha}{p} + frac{3}{q} leq 2 alpha - frac{3}{2},...

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Main Author:	Yuwen Luo
Format:	Article
Language:	English
Published:	Texas State University 2010-08-01
Series:	Electronic Journal of Differential Equations
Subjects:	Generalized Navier-Stokes equation regularity Serrin criteria
Online Access:	http://ejde.math.txstate.edu/Volumes/2010/105/abstr.html

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spelling	doaj-9023b4c4095c4e2cbba23ea363486fa22020-11-24T21:08:39ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912010-08-012010105,15Regularity of generalized Naveir-Stokes equations in terms of direction of the velocityYuwen LuoIn this article, the author studies the regularity of 3D generalized Navier-Stokes (GNS) equations with fractional dissipative terms $(-Delta)^{alpha} u$. It is proved that if $hbox{div} (u / \|u\|) in L^p (0, T ; L^q (mathbb{R}^3))$ with $$ frac{2 alpha}{p} + frac{3}{q} leq 2 alpha - frac{3}{2},quad frac{6}{4 alpha-3} < q leq infty . $$ then any smooth on GNS in $[0,T)$ remains smooth on $[0, T]$. http://ejde.math.txstate.edu/Volumes/2010/105/abstr.htmlGeneralized Navier-Stokes equationregularitySerrin criteria
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Yuwen Luo
spellingShingle	Yuwen Luo Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity Electronic Journal of Differential Equations Generalized Navier-Stokes equation regularity Serrin criteria
author_facet	Yuwen Luo
author_sort	Yuwen Luo
title	Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity
title_short	Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity
title_full	Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity
title_fullStr	Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity
title_full_unstemmed	Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity
title_sort	regularity of generalized naveir-stokes equations in terms of direction of the velocity
publisher	Texas State University
series	Electronic Journal of Differential Equations
issn	1072-6691
publishDate	2010-08-01
description	In this article, the author studies the regularity of 3D generalized Navier-Stokes (GNS) equations with fractional dissipative terms $(-Delta)^{alpha} u$. It is proved that if $hbox{div} (u / \|u\|) in L^p (0, T ; L^q (mathbb{R}^3))$ with $$ frac{2 alpha}{p} + frac{3}{q} leq 2 alpha - frac{3}{2},quad frac{6}{4 alpha-3} < q leq infty . $$ then any smooth on GNS in $[0,T)$ remains smooth on $[0, T]$.
topic	Generalized Navier-Stokes equation regularity Serrin criteria
url	http://ejde.math.txstate.edu/Volumes/2010/105/abstr.html
work_keys_str_mv	AT yuwenluo regularityofgeneralizednaveirstokesequationsintermsofdirectionofthevelocity
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Regularity of generalized Naveir-Stokes equations in terms of direction of the velocity

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