The end-point regularity criterion for the Navier–Stokes equations in terms of ∂3u. (October 2020) - Skalak, Zdenek
Abstract: We show the following extension of the recent optimal regularity results by Kukavica & Ziane, Cao and Zhang: If u is a solution of the Navier–Stokes equations in the whole space R 3 and ∂ 3 u ∈ L p ( 0, T ; L q ( R 3 ) ), T > 0, where 2 ∕ p + 3 ∕ q = 2 and q ∈ ( 3 ∕ 2, 3 ], then u is regular on ( 0, T ] .