| Abstract: |
| Viscoelastic rate-type fluid models involving the stress and its observer-invariant time derivatives of higher order are used to describe the behaviour of materials with complex microstructure: geomaterials like asphalt, biomaterials such as vitreous in the eye, synthetic rubbers such as styrene butadiene rubber. A standard model that belongs to the category of viscoelastic rate-type fluid models of the second order is the model due to Burgers, which can be viewed as a mixture of two Oldroyd-B models of the first order. This viewpoint allows one to develop the whole hierarchy of generalized models of the Burgers type. We study such generalizations that can be viewed as a combination (mixture) of several classical viscoelastic models having in general two different relaxation mechanisms. We discuss the conditions guaranteeing the global in time and large data existence of a weak solution as well as the conditions for regularity and the (in)stability of the solution. |
|