Global existence results for some viscoelastic models with an integral constitutive law

2013/11/29 by Laurent Chupin, Chupin, Laurent
Engineering · Mathematics · #Elasticity and Material Modeling #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #math.AP

paper · pdf · doi:10.48550/arxiv.1311.7569

arxiv created 2013/11/29 · arxiv updated 2013/12/02

Abstract

We provide a proof of global regularity of solutions of some models of viscoelastic flow with an integral constitutive law, in the two spatial dimensions and in a periodic domain. Models that are included in these results are classical models for flow memory: for instance some K-BKZ models, the PSM model or the Wagner model. The proof is based on the fact that these models naturally give a L^∞-bound on the stress and that they allow to control the spatial gradient of the stress. The main result does not cover the case of the Oldroyd-B model.

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