Some elementary estimates for the Navier-Stokes system
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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 $H^{\frac {1}{2}}({\mathbb {T}}^3)$.References
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Additional Information
- Jean Cortissoz
- Affiliation: Departamento de Matemáticas, Universidad de Los Andes, Bogotá DC, Colombia
- Email: jcortiss@uniandes.edu.co
- Received by editor(s): October 14, 2008
- Published electronically: May 29, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 3343-3353
- MSC (2000): Primary 35Q30
- DOI: https://doi.org/10.1090/S0002-9939-09-09989-4
- MathSciNet review: 2515404