A Classical Blow up Criterion to Cauchy Problem for the Micropolar Fluid Flows

Abstract

In this paper, we discuss the cauchy problem of the viscous micropolar fluid flow model in 2D. This note obtains a classical regularity blow up criterion for the two-dimensional micropolar fluid flows. When the inital data is allowed to the suitable Sobolev space, for the life span 𝑇 𝑚𝑎𝑥 , it is worth noting that the result holds ∫ ‖𝛻𝑢(𝑡)‖ 𝐿 ∞ 𝑑𝑡 = 0 𝑇 𝑚𝑎𝑥 0 .