We characterize a possible blowup for the 3D Navier-Stokes on the basis of dynamical equations for vector potentials A. This is motivated by a known interpolation parallel to A parallel to(BMO) <= parallel to u parallel to(3)(L), together with recent mathematical results. First, by working out an inversion formula for singular integrals that appear in the governing equations, we derive a criterion using the nonlinear term of A as integral(t*)(0) parallel to partial derivative A/partial derivative t - nu Delta A parallel to(infinity)(L) dt = infinity for a blowup at t(*). Second, for a particular form of a scale-invariant singularity of the nonlinear term we show that the vector potential becomes unbounded in its L-infinity and BMO norms. Using the stream function, we also consider the 2D Navier-Stokes equations to seek an alternative proof of their known global regularity. It is not yet proven that the BMO norm of vector potentials in 3D (or, the stream function in 2D) serve as a blow up criterion in more general cases. (C) 2017 Author(s).