Hyperbolicity and change of type in the flow of viscoelastic fluids. (English) Zbl 0572.76011
The equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators. Propagation of singularities is discussed and conditions for a change of type are investigated. The vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied. This leads to a partitioning of the field of flow into subcritical and supercritical regions, as in the problem of transonic flow.
MSC:
| 76A10 | Viscoelastic fluids |
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
Keywords:
classification of differential operators; slip surface propagation; upper convected Maxwell fluid; Oldroyd fluid; simple fluids with fading memory; Propagation of singularities; change of type; vorticity equation for steady flowReferences:
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