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Ideal density‐dependent incompressible viscoelastic flow in the critical Besov spaces
Author(s) -
Hua Qiu,
Fang Shaomei
Publication year - 2018
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.4877
Subject(s) - mathematics , besov space , ideal (ethics) , viscoelasticity , bounded function , compressibility , mathematical analysis , space (punctuation) , zero (linguistics) , dimension (graph theory) , flow (mathematics) , pure mathematics , geometry , interpolation space , mechanics , functional analysis , physics , biochemistry , chemistry , philosophy , epistemology , gene , thermodynamics , linguistics
In this paper, we consider the well‐posedness issue for the density‐dependent incompressible viscoelastic fluids of the Oldroyd model for the ideal case in space dimension greater than 2. We obtain the local well‐posedness of this model under the assumption that the initial density is bounded away from zero in the critical Besov spaces by means of the Littlewood‐Paley theory and Bony's paradifferential calculus. In particular, we obtain a Beale‐Kato‐Majida–type regularity criterion.