Logarithmically improved regularity criterion for the 3D micropolar fluid equations (Q1637830)

Summary: We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies \(\int^T_0(\|\nabla\times u\|_{\dot B{}^0_{\infty,\infty}}/\sqrt{1+\log(1+\|\nabla\times u\|_{\dot B{}^0_{\infty,\infty}}))}dt<\infty\) then the strong solution can be smoothly extended after time \(T\).