Speaker: **Michal Bathory**

Title: **Existence analysis of rate-type viscoelastic fluids with stress diffusion**

Abstract: In the talk, we will first recall some standard models for unsteady flows of incompressible viscoelastic fluids, such as the Navier-Stokes coupled with Oldroyd-B or Giesekus models. Then, we will discuss the main difficulties that arise when one tries to prove an existence of a weak solution for such models. And finally, we show how to get around these difficulties by strengthening of the dissipation, or of the energy storage mechanism.

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*Speaker*: **Helena Švihlová and Jaroslav Hron**

*Title*: **Computational study of hemodynamical flow in cerebral aneurysms and common carotid artery**

*Abstract*: We will give overview of two hemodynamical flow problems, namely the flow in cerebral aneurysm and flow in common carotid artery, where the medical community can benefit from the knowledge of the flow fields. In both cases it is well well established that hemodynamics has a significant role in possible further evolution of unphysiological conditions, like growth or rupture of the aneurysm or growth or deposit of a plaque in the carotid artery.

We will present assumptions and limitations of the models used in CFD computations as well as the potential benefits in a clinical practice in a near future. We will discuss the limitations at different levels of the blood flow modeling and our experience with setup of computational methods using academic open source computational tools (PETSc, FEniCS, VMTK).

We will describe certain intermediate steps like image segmentation and boundary condition extraction as well as extension of the models to non-newtonian behavior of the blood and possible vessel wall interactions. We will briefly discuss the numerical methods in context of high performance computing.

In this second part of the seminar Klára Kalousová, Kathryn Lund, Malte Kampschulte and Giovanni Gravina will give a talk.

For more details see: http://mathmac.cuni.cz/2018-2023/wp-content/uploads/2019/11/UNCE_MathMAC-Seminar_2019-11-1.pdf

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The first part of junior researchers will present their works. The next two seminars (December 2 and December 9) will consist of the other talks. For more details see: http://mathmac.cuni.cz/2018-2023/wp-content/uploads/2019/11/UNCE_MathMAC-Seminar_2019-11-1.pdf

Speaker: **Tomáš Los**

Title: **On planar flows of viscoelastic fluids of Burgers type**

Abstract: Viscoelastic rate-type fluid models involving the stress and its observer-invariant time derivatives of higher order are used to describe materials with complex microstructure, for example geomaterials like asphalt, biomaterials such as vitreous in the eye, mussels. A standard model that belongs to the category of viscoelastic rate-type fluid models of second order is the model due to Burgers that 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 a Burgers type. We study one such generalization. Carrying on the study by Massmoudi (2011), who briefly prove weak sequential stability of solutions to the Giesekus model, we prove long time and large data existence of weak solutions to a mixture of two Giesekus models in two spatial dimensions.

]]>Speaker: **Miroslav Bulíček**

Title: **Mathematical analysis of viscoelastic fluids with stress diffusion**

Abstract: We discuss the long-time existence of weak solutions for large-data to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a viscoelastic rate-type model with a stress-diffusion term. We focus on the thermodynamical compatibility of the models and propose also the proper convergence scheme that will lead to the existence of a solution.

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