# Stationary Oldroyd model with diffusive stress: mathematical analysis of the model and vanishing diffusion process

Abstract : In this paper we address the stationary Oldroyd model with diffusive stress in two ways: first we present the mathematical analysis of the model. Second, as the link between the diffusive model and the standard one is questionable from the mathematical point of view, we discuss, by means of numerical simulations, the behaviour of the model with respect to vanishing diffusion. In particular, numerical results in 2D or 3D suggest that the solution of the diffusive model converges to the solution of the non-diffusive model at order 1 in the $L^2-$norm and $H^1-$norm.
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Journal articles
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https://hal.archives-ouvertes.fr/hal-00905096
Contributor : Sébastien Martin <>
Submitted on : Sunday, March 8, 2015 - 11:48:19 PM
Last modification on : Friday, September 20, 2019 - 4:34:03 PM
Long-term archiving on: Monday, April 17, 2017 - 3:51:14 AM

### File

CM_Oldroyd_v8.pdf
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### Identifiers

• HAL Id : hal-00905096, version 2
• ARXIV : 1311.4032

### Citation

Laurent Chupin, Sébastien Martin. Stationary Oldroyd model with diffusive stress: mathematical analysis of the model and vanishing diffusion process. Journal of Non-Newtonian Fluid Mechanics, Elsevier, 2015, 218, pp.27-39. ⟨hal-00905096v2⟩

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