Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. (English) Zbl 1159.35396
Summary: 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 \(L^{p,q}_{x,t}\) source with \(3/p+2/q\leq 2\), \(2<q\leq \infty\), \((p,q)\neq (3/2,\infty)\) 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 additional integral conditions.
MSC:
| 35Q30 | Navier-Stokes equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35D10 | Regularity of generalized solutions of PDE (MSC2000) |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
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