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Some elementary estimates for the Navier-Stokes system

Author(s): Jean Cortissoz
Journal: Proc. Amer. Math. Soc. 137 (2009), 3343-3353.
MSC (2000): Primary 35Q30
Posted: 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 $H^{\frac{1}{2}}({\mathbb{T}}^3)$ .

References:

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