We study the interior regularity of weak solutions of the incompressible Navier-Stokes equations in Ω × (0, T), where Ω ⊂ R 3 and 0 < T < ∞. The local boundedness of a weak solution u is proved under the assumption that ||u||Lws(0, T; Lwr (Ω)) is sufficiently small for some (r, s) with 2/s + 3/r = 1 and 3 ≤ r ≤ ∞. Our result extends the well-known criteria of Serrin (1962), Struwe (1988) and Takahashi (1990) to the weak space-time spaces.
ASJC Scopus subject areas
- 数学 (全般)