Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in R 3
Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in R 3
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DOI：
10.1016/j.jde.2005.06.001
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发表时间：
2005-09
影响因子：
2.4
通讯作者：
Zhifei Zhang;Qionglei Chen
中科院分区：
文献类型：
--
作者：
Zhifei Zhang;Qionglei Chen
我们考虑了R3中Navier-Stokes方程弱解的正则性。设u是R3×（0，T）中的弱解，w=curlu，且w ∈ =（w1，w2，0）.证明了当2/q+3/r= 2，32 <r <$∞，σ <$2r/3时，若w <$∈Lq（0，T;B stecr，σ0），u成为经典解.本文改进了Kozono-Yatsu [3D Navier-Stokes方程强解的涡量双分量延拓准则，Math. Z. J. J.]的结果。246（2003）55-68]。
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].