Global Solutions to the 2-Dimensional Incompressible Oldroyd-B Model with Hybrid Dissipation and Partial Damping on Stress Tensor

Abstract

In this paper, we derive an incompressible Oldroyd-B model with hybrid dissipation and partial damping on stress tensor $$\tau $$ via the velocity equations and the generalized constitutive law so that global well-posedness of the model is established in the Sobolev space framework. Precisely speaking, the proof is based on the curl-div free property of $$\tau - {\nabla }\frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau - ( {\nabla } \frac{1}{\Delta } \mathbb {P}\mathrm{div}\tau )^T $$ , the low frequency dissipation and high frequency damping of $$\tau $$ and the dissipation of u.