Initial Value Problems for Viscoelastic Liquids.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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 infinity-smoothing coexists with finite wave speeds. Author
- Numerical Mathematics
- Fluid Mechanics