Some elementary estimates for the Navier-Stokes system

Cortissoz, Jean

doi:10.1090/S0002-9939-09-09989-4

Some elementary estimates for the Navier-Stokes system
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Proc. Amer. Math. Soc. 137 (2009), 3343-3353 Request permission

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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