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

Abstract

This paper presents a new small data global well-posedness result on the incompressible Oldroyd-B model with only dissipation in the equation of stress tensor (without stress tensor damping or velocity dissipation). The dissipation is not necessarily given by the standard Laplacian operator and any fractional dissipation with fractional power equal to or greater than 1/2 suffices. The functional setting is the hybrid homogeneous Besov spaces, which allow us to maximize the functional spaces of the initial data.