Special Session 2: New frontiers in the compressible mathematical fluid mechanics and thermodynamics

Existence results for thermoviscoelastic fluid models
Miroslav Bul\\'{\\i}\\v{c}ek
Charles University
Czech Rep
Co-Author(s):    
Abstract:
We present theoretical results on two classes of thermodynamically consistent models for heat-conducting viscoelastic fluids: (i) rate-type models of Giesekus type, and (ii) kinetic models based on the Fokker–Planck equation for dilute polymeric solutions. For both frameworks, we establish the existence of global weak solutions under natural assumptions on initial data and demonstrate their stability properties. The analysis rigorously captures key aspects of viscoelastic and thermal behavior, including energy storage and entropy production, providing a solid foundation for the study of complex materials with coupled viscous, elastic, and thermal effects.