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Ladder estimates for micropolar fluid equations and regularity of global attractor
Author(s) -
Szopa Piotr
Publication year - 2010
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1277
Subject(s) - mathematics , attractor , domain (mathematical analysis) , order (exchange) , inequality , pure mathematics , first order , mathematical analysis , finance , economics
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.