On the IAA version of the Doi-edwards model versus the K-BKZ rheological model for polymer fluids: a global existence result for shear flows with small initial data. (English) Zbl 1386.76013
Summary: This paper establishes the existence of smooth solutions for the Doi-Edwards rheological model of viscoelastic polymer fluids in shear flows. The problem turns out to be formally equivalent to a K-BKZ equation but with constitutive functions spanning beyond the usual mathematical framework. We prove, for small enough initial data, that the solution remains in the domain of hyperbolicity of the equation for all \(t\).
MSC:
| 76A10 | Viscoelastic fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
| 82D60 | Statistical mechanics of polymers |
Keywords:
Doi-Edwards polymer model; K-BKZ viscoelastic fluid; shear flows; convolution operator; evolutionary integro-differential equationReferences:
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