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

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 View the MathML sourceB2,∞s with View the MathML sources>d2, and which implies global well-posedness for small data in HsHs with View the MathML sources>d2, since the Sobolev space HsHs is embedded in View the MathML sourceB2,∞s.