On the regularity of the solutions of the Navier–Stokes equations via one velocity component

We consider the regularity criteria for the incompressible Navier--Stokes equations connected with one velocity component. Based on the method from Cao and Titi (2008 Indiana Univ. Math. J. 57 2643--61) we prove that the weak solution is regular, provided , , \frac {10}{3} ' src='http://ej...

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Bibliographic Details
Published in:Nonlinearity 2010-05, Vol.23 (5), p.1097-1107
Main Authors: Zhou, Yong, Pokorný, Milan
Format: Article
Language:English
Subjects:
Alignment
Criteria
Exact sciences and technology
Fluid flow
Global analysis, analysis on manifolds
Infinity
Mathematical analysis
Mathematical methods in physics
Mathematics
Nonlinearity
Other topics in mathematical methods in physics
Partial differential equations
Physics
Regularity
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:We consider the regularity criteria for the incompressible Navier--Stokes equations connected with one velocity component. Based on the method from Cao and Titi (2008 Indiana Univ. Math. J. 57 2643--61) we prove that the weak solution is regular, provided , , \frac {10}{3} ' src='http://ej.iop.org/images/0951-7715/23/5/004/non327722in003.gi f ' align=middle> or provided , if or if s (3, {infinity}]. As a corollary, we also improve the regularity criteria expressed by the regularity of or .
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/23/5/004