# Viscoelastic flows of Maxwell fluids with conservation laws

@article{Boyaval2020ViscoelasticFO, title={Viscoelastic flows of Maxwell fluids with conservation laws}, author={S{\'e}bastien Boyaval}, journal={ESAIM: Mathematical Modelling and Numerical Analysis}, year={2020}, volume={55}, pages={807-831} }

We consider multi-dimensional extensions of Maxwell’s seminal rheological equation for 1D viscoelastic flows. We aim at a causal model for compressible flows, defined by semi-group solutions given initial conditions, and such that perturbations propagate at finite speed. We propose a symmetric hyperbolic system of conservation laws that contains the Upper-Convected Maxwell (UCM) equation as causal model. The system is an extension of polyconvex elastodynamics, with an additional material metric…

## 4 Citations

### Non-isothermal viscoelastic flows with conservation laws and relaxation

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Maxwell models for viscoelastic flows are famous for their potential to unify elastic motions of solids with viscous motions of liquids in the continuum mechanics perspective. But the usual Maxwell…

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