On the global existence for a regularized model of viscoelastic non-Newtonian fluid

Abstract

We study the generalized Oldroyd model with viscosity depending on the shear stress behaving like $\mu (\mathbf{D})\sim |\mathbf{D}{|}^{p-2}$ ($p>\frac{6}{5}$) regularized by a nonlinear stress diffusion. Using the Lipschitz truncation method we are able to prove global existence of weak solution to the corresponding system of partial differential equations.