Abstract
We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω×(0,T), where Open image in new window and 0<T<∞. The local boundedness of a weak solution u is proved under the assumption that Open image in new window is sufficiently small for some (r,s) with Open image in new window and 3≤r<∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.
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