Two new regularity criteria for nematic liquid crystal flows

In this study, we present two new regularity criteria for three-dimensional nematic liquid crystal flows. More precisely, we show that if ∂3u∈Lβ(0,T;Lα(R3))∂3u∈Lβ(0,T;Lα(R3)) with 2β+3α≤3(α+2)4α (α>2α>2), or u3u3, ∇d∈Lβ(0,T;Lα(R3))∇d∈Lβ(0,T;Lα(R3)) with 2β+3α≤34+12α (α>103), then the corresponding weak solution (u,d)(u,d) can be extended beyond T.