Ladder estimates for micropolar fluid equations and regularity of global attractor

This paper is devoted to obtain ladder inequalities for 2D micropolar fluid equations on a periodic domain Q =(0, L ) 2 . The ladder inequalities are differential inequalities that connect the evolution of L 2 norms of derivatives of order N with the evolution of the L 2 norms of derivatives of other (usually lower) order. Moreover, we find (with slight assumption on external fields) long‐time upper bounds on the L 2 norms of derivatives of every order, which implies that a global attractor is made up from C ∞ functions. Copyright © 2010 John Wiley & Sons, Ltd.