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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 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 -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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