微极流方程组强解的爆破准则

Blow up criterion for the 3D Micropolar fluid equations

利用Littlewood-Paley分解技巧结合能量估计的方法,改进了微极流方程强解的爆破准则.具体地,如果速度场的旋度水平部分:Ω=■×u,Ω=(Ω1,Ω2,0)满足∫0^T∥■(t)∥Ω∞,∞0 dt<∞,则强解一定能够延拓到T=+∞.

By means of the Littlewood-Paley decomposition,a Beale-Kato-Majda type blow-up criterion of strong solution to 3 D Micropolar fluid equations is improved.It is proved that if∫0^T∥Ω(t)∥■∞,∞0 dt<∞,then the strong solution can be extended at t=T,whereΩ=■×u and■=(Ω1,Ω2,0).