On planar flows of viscoelastic fluids of Giesekus type

• Published in: Nonlinearity Vol. 35; no. 12; pp. 6557 - 6604
• Main Authors: Bulíček, Miroslav, Los, Tomáš, Lu, Yong, Málek, Josef
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.12.2022
• Subjects: Burgers model; Giesekus model; large-data existence; long-time existence; viscoelasticity; weak solution
• ISSN: 0951-7715; 1361-6544
• DOI: 10.1088/1361-6544/ac9a2c

Viscoelastic rate-type fluid models 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 one such generalization that can be viewed as a combination (mixture) of two Giesekus viscoelastic models having in general two different relaxation mechanisms. We prove, in two spatial dimensions, long-time and large-data existence of weak solutions to the considered generalization of the Burgers model subject to no-slip boundary condition. We also provide, as a particular case, a complete proof of global-in-time existence of weak solutions to the Giesekus model in two spatial dimensions.