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Viscous Incompressible Flows Under Stress-Free Boundary Conditions. The Smoothness Effect of Near Orthogonality

H. Beirão da Veiga — 2012

Bollettino dell'Unione Matematica Italiana

We consider the initial boundary value problem for the 3D Navier-Stokes equations under a slip type boundary condition. Roughly speaking, we are concerned with regularity results, up to the boundary, under suitable assumptions on the directions of velocity and vorticity. Our starting point is a recent, interesting, result obtained by Berselli and Córdoba concerning the ``near orthogonal case''. We also consider a ``near parallel case''.

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