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Existence and asymptotic behavior for an incompressible Newtonian flow with intrinsic degree of freedom
Author(s) -
He Cheng,
Zhou Daoguo
Publication year - 2013
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.2880
Subject(s) - mathematics , compressibility , newtonian fluid , norm (philosophy) , initial value problem , mathematical analysis , dimension (graph theory) , homogeneous , non newtonian fluid , degree (music) , cauchy problem , flow (mathematics) , classical mechanics , pure mathematics , geometry , combinatorics , physics , mechanics , political science , acoustics , law
We consider the Cauchy problem of a mathematical model for an incompressible, homogeneous, Newtonian fluid taking into account internal degrees of freedom. We first show that there exists a unique global strong solution when the given initial data are small in some sense. Then, we deduce the optimal decay rates for velocity vector in L 2 − norm and L p − norm for p > n . These decay estimates depend only on the spatial dimension and the decay properties of the heat solution with the same data. Copyright © 2013 John Wiley & Sons, Ltd.