Interior regularity criteria in weak spaces for the Navier-Stokes equations

초록

We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Omega x (0, T), where Omega subset of R-3 and 0 < T < infinity. The local boundedness of a weak solution u is proved under the assumption that parallel touparallel to(Lw)((0,T; Lw)((Omega)))(s)(r) is sufficiently small for some (r, s) with 2/s + 3/r = 1 and 3 less than or equal to r < infinity. 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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