Tanner Duality Between the Oldroyd–Maxwell and Grade-two Fluid Models

We prove an asymptotic relationship between the grade-two fluid model and a class of models for non-Newtonian fluids suggested by Oldroyd, including upper-convected lower-convected Maxwell models. This confirms earlier observation Tanner. provide new interpretation temporal instability negative coefficients. Our techniques allow simple proof convergence steady to Navier–Stokes as α→0 (under suitable conditions) in three dimensions. They also Oldroyd their parameters tend zero.