Vanishing viscosity limit of the 3D incompressible Oldroyd-B model

Abstract

Consider the vanishing viscosity limit of the 3D incompressible Oldroyd-B model. It is shown that this set of equations admits a unique global solution with small analytic data uniformly in the coupling parameter $\omega$ close to $1$ that corresponds to the inviscid case. We justify the limit from the Oldroyd-B model to the inviscid case $\omega =1$ for all time. Moreover, if the nonlinear term $g_{\alpha }(\tau ,\nabla u)$ is ignored, similar results hold without resorting to the analytic regularity.