| 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. |
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