# Initial value problems for viscoelastic liquids

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## Abstract

Cauchy problems for equations modelling non-Newtonian fluids are discussed and recent existence theorems for classical solutions, based on semigroup methods, are presented. Such existence results depend in a crucial manner on the symbol of the leading differential operator. Both “parabolic” and “hyperbolic” cases are discussed. In general, however, the leading differential operator may be of non-integral order, arising from convolution with a singular kernel. This has interesting implications concerning the propagation of singularities. In particular, there are cases where C^{∞}-smoothing coexists with finite wave speeds.

## Keywords

Evolution Problem Stokes Operator Quasilinear Parabolic Equation Fading Memory Viscoelastic Liquid
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© Springer-Verlag 1984