LOCAL REGULARITY OF THE STEADY STATE NAVIER-STOKES EQUATIONS NEAR BOUNDARY IN FIVE DIMENSIONS

Abstract

We present a new regularity criterion for suitable weak solutions of the steady-state Navier-Stokes equations near boundary in dimension five. We show that suitable weak solutions are regular 5 up to the boundary if the scaled L 2 −norm of the solution is small near the boundary. Our result is also valid in the interior.

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