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We formulate sufficient conditions for regularity up to the boundary of a weak solution v in a subdomain Ω× (t1, t2) of the time-space cylinder Ω× (0, T ) by means of requirements on one of the eigenvalues of the rate of deformation tensor. We assume that Ω is a cube.

Estimates up to the boundary of a weak solution to the Navier–Stokes equation in a cube in dependence on eigenvalues of the rate of deformation tensor