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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some elementary estimates for the Navier-Stokes system


Author: Jean Cortissoz
Journal: Proc. Amer. Math. Soc. 137 (2009), 3343-3353
MSC (2000): Primary 35Q30
Published electronically: May 29, 2009
MathSciNet review: 2515404
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Abstract: In this paper we study the incompressible Navier-Stokes equations in $ {\mathbb{T}}^3=[0,1]^3$ with periodic boundary conditions. We show that a weak solution of the Navier-Stokes equations that is small in $ L^{\infty}(0,T;\Phi(2))$ is also smooth. We also give elementary proofs of some classical regularity results for the Navier-Stokes equations involving the Sobolev space $ H^{\frac{1}{2}}({\mathbb{T}}^3)$.


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Additional Information

Jean Cortissoz
Affiliation: Departamento de Matemáticas, Universidad de Los Andes, Bogotá DC, Colombia
Email: jcortiss@uniandes.edu.co

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09989-4
PII: S 0002-9939(09)09989-4
Keywords: Navier-Stokes equations, regularity
Received by editor(s): October 14, 2008
Published electronically: May 29, 2009
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.