TANNER DUALITY BETWEEN THE OLDROYD-MAXWELL AND GRADE-TWO FLUID MODELS

Vivette Girault (1) , L Ridgway Scott (2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 Department of Computer Science, University of Chicago

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

Domaines: Mathématiques [math]

Vivette Girault, L Ridgway Scott. TANNER DUALITY BETWEEN THE OLDROYD-MAXWELL AND GRADE-TWO FLUID MODELS. Comptes Rendus. Mathématique, 2021, 359 (9), pp. 1207-1215. ⟨10.5802/crmath.269⟩. ⟨hal-03910968⟩