Global Existence Results for Some Viscoelastic Models with an Integral Constitutive Law

We provide a proof of global regularity of solutions of some models of viscoelastic flow with an integral constitutive law in 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 an L ∞ -bound on the stress and that they allow one 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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