On non-isothermal flows of dilute incompressible polymeric fluids

Abstract: In the first part of the talk, we show that thermodynamically consistent models for non-isothermal flows of such fluids can be derived in a very elementary manner. Our approach is based on identifying the energy storage mechanisms and entropy production mechanisms in the fluid of interest, which in turn leads to explicit formulae for the Cauchy stress tensor and for all the fluxes involved. Having identified these mechanisms, we first derive the governing system of nonlinear partial differerential equations coupling the unsteady incompressible temperature-dependent Navier–Stokes equations with a temperature-dependent generalization of the classical Fokker–Planck equation and an evolution equation for the internal energy. In the second - main part - of the talk, we show that sequences of smooth solutions to the initial–boundary-value problem, which satisfy the underlying energy/entropy estimates (and their consequences in connection with the governing system of PDEs), converge to weak solutions that satisfy a renormalized entropy inequality. The talk is based on joint results with Miroslav Bulíček, Mark Dostalík, Vít Průša and Endré Süli.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)