On Regularity of a Weak Solution to the Navier-Stokes Equations with the Generalized Navier Slip Boundary Conditions

The paper shows that the regularity up to the boundary of a weak solution v of the Navier-Stokes equation with generalized Navier's slip boundary conditions follows from certain rate of integrability of at least one of the functions zeta(1), (zeta(2))(+) (the positive part of zeta(2)), and zeta(3), where zeta(1) <= zeta(2) <= zeta(3) are the eigenvalues of the rate of deformation tensor D(v). A regularity criterion in terms of the principal invariants of tensor D(v) is also formulated.