M ay 2 00 5 Regularity criteria for suitable weak solutions of the Navier - Stokes equations near the boundary

We present some new regularity criteria for “suitable weak solutions” of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are Hölder continuous up to the boundary provided that the scaled mixed norm L x,t with 3/p + 2/q ≤ 2, 2 < q ≤ ∞, (p, q) 6= (3/2,∞), is small near the boundary. Our methods yield new results in the interior case as well. Partial regularity of weak solutions is also analyzed under some conditions of the Prodi-Serrin type.