Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary
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Any weak solution u of the Navier-Stokes equations in a bounded domain satisfying the Prodi-Serrin's conditions locally near the smooth boundary cannot have singular points there. This local-up-to-the-boundary boundedness of u in space-time implies the Holder continuity of u up-to-the-boundary in the space variables.
CitationSkalak, Z. (2005). Regularity of weak solutions of the Navier-Stokes equations near the smooth boundary. Electronic Journal of Differential Equations, 2005(45), pp. 1-11.
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