Global regularity for the generalized incompressible Oldroyd-B model with only stress tensor dissipation in critical Besov spaces (Q2669931)

In this excellent paper, a global well-posedness result for a generalized incompressible Oldroyd-B model, with only dissipation in the equation of stress tensor, is obtained in critical Besov spaces in the case of small data. The proof of this result is based on establishing a global bound of the solution. As an essential step in the proof, a suitable energy functional consisting of four parts is defined. The functional setting is the hybrid homogeneous Besov spaces, which allow large functional spaces of initial data.