In this paper, we revise Maxwells constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice conservation-dissipation (relaxation) structure and therefore is symmetrizable hyperbolic. Moreover, for smooth flows we rigorously verify that the revised Maxwells constitutive relations are compatible with Newtons law of viscosity.
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