When, where: **Monday October 1, 2018, in K3 from 9:00 till 10:30. **

Speaker: **Josef Málek**

Title: **PDE analysis for a class of thermodynamically compatible viscoelastic rate-type fluids with stress-diffusion **

Abstract: We establish the long-time existence of large-data weak solutions to a system of nonlinear partial differential equations. The system of interest governs the motion of non-Newtonian fluids described by a simplified viscoelastic rate-type model with a stress-diffusion term. The simplified model shares many qualitative features with more complex

viscoelastic rate-type models that are frequently used in the modeling of fluids with complicated microstructure.

As such, the simplified model provides important preliminary insight into the mathematical properties of these more complex and practically relevant models of non-Newtonian fluids. The simplified model that is analyzed from the mathematical perspective is shown to be thermodynamically consistent.

We present the results regarding existence of global–in–time weak solutions for any finite energy initial data both for incompressible and compressible fluids.

The lecture is based on the results achieved together with M. Bulíček, E. Feireisl, V. Průša and E. Süli.