Abstract
In this paper, we study the viscoelastic fluid system of the Oldroyd model. By means of the Fourier frequency localization and Bony paraproduct decomposition, we establish the local well-posedness for the incompressible Oldroyd system in the critical Besov spaces under the ideal case. Furthermore, as a byproduct, we obtain a Beale–Kato–Majida-type criterion (Beale et al., 1984).
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