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Existence of global strong solution to the micropolar fluid system in a bounded domain
Author(s) -
Yamaguchi Norikazu
Publication year - 2005
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.617
Subject(s) - mathematics , resolvent , semigroup , bounded function , domain (mathematical analysis) , analytic semigroup , initial value problem , nonlinear system , mathematical analysis , boundary value problem , physics , quantum mechanics
In this paper we are concerned with the initial boundary value problem of the micropolar fluid system in a three dimensional bounded domain. We study the resolvent problem of the linearized equations and prove the generation of analytic semigroup and its time decay estimates. In particular, L p – L q type estimates are obtained. By use of the L p – L q estimates for the semigroup, we prove the existence theorem of global in time solution to the original nonlinear problem for small initial data. Furthermore, we study the magneto‐micropolar fluid system in the final section. Copyright © 2005 John Wiley & Sons, Ltd.