BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Josef Málek DTSTART:20251015T070000Z DTEND:20251015T080000Z DTSTAMP:20260422T122225Z UID:MathMAC/40 DESCRIPTION:Title: On non-isothermal flows of dilute incompressible polymeric fluids\nby Josef Málek as part of Modelling of materials - theory\, model reduction and efficient numerical methods (UNCE MathMAC)\n\n\nAbstract\nIn the firs t part of the talk\, we show that thermodynamically consistent models for non-isothermal flows of such fluids can be derived in a very elementary ma nner. Our approach is based on identifying the energy storage mechanisms a nd entropy production mechanisms in the fluid of interest\, which in turn leads to explicit formulae for the Cauchy stress tensor and for all the fl uxes involved. Having identified these mechanisms\, we first derive the go verning system of nonlinear partial differerential equations coupling the unsteady incompressible temperature-dependent Navier–Stokes equations wi th 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 energ y/entropy estimates (and their consequences in connection with the governi ng system of PDEs)\, converge to weak solutions that satisfy a renormalize d entropy inequality. The talk is based on joint results with Miroslav Bul íček\, Mark Dostalík\, Vít Průša and Endré Süli.\n LOCATION:https://researchseminars.org/talk/MathMAC/40/ END:VEVENT END:VCALENDAR