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.
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Renardy, M. (1984). Initial value problems for viscoelastic liquids. In: Ciarlet, P.G., Roseau, M. (eds) Trends and Applications of Pure Mathematics to Mechanics. Lecture Notes in Physics, vol 195. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12916-2_65
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DOI: https://doi.org/10.1007/3-540-12916-2_65
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