Global well-posedness of viscoelastic fluids of Oldroyd type in Besov spaces

We investigate a system of equations concerning an incompressible viscoelastic fluid of the Oldroyd type which describes one class of non-Newtonian fluid with memory. Making use of a regularization method in conjunction with Bony’s paraproduct decomposition, we obtain the existence and uniqueness of a small global solution for the above system in the Besov spaces B2,∞s with s>d2, and which implies global well-posedness for small data in HsHs with s>d2, since the Sobolev space HsHs is embedded in B2,∞s.