Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in R 3

By Zhifei Zhang, Qionglei Chen. 2005

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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].

Subfields: Applied Mathematics, Mathematical Physics

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