Title: Regularity criterion via two components of vorticity on weak solutions to the Navier–Stokes equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:math>
Abstract: We consider the regularity of weak solutions to the Navier–Stokes equations in R3. Let u be a weak solution in R3×(0,T), w=curlu, and w˜=(w1,w2,0). It is proved that u becomes a classical solution if w˜∈Lq(0,T;B˙r,σ0), for 2/q+3/r=2,32<r⩽∞, and σ⩽2r/3. This is an improvement of the result given by Kozono–Yatsu [Extension criterion via two-components of vorticity on strong solution to the 3D Navier–Stokes equations, Math. Z. 246 (2003) 55–68].