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},quad...

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Bibliographic Details
Published inElectronic journal of differential equations Vol. 2010; no. 105; pp. 1 - 5
Main Author Yuwen Luo
Format Journal Article
LanguageEnglish
Published Texas State University 02.08.2010
Subjects
Generalized Navier-Stokes equation
regularity
Serrin criteria
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Summary: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 $[0, T]$.
ISSN:1072-6691
1072-6691