Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature

• Published in: Mathematics and computers in simulation Vol. 189; pp. 5 - 20
• Main Authors: Dostalík, Mark, Průša, Vít, Stein, Judith
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2021
• Subjects: Finite amplitude stability; Heat conducting fluid; Non-equilibrium steady state; Thermodynamically open system; Viscoelastic fluid; Viscoelastic fluid; Non-equilibrium steady state; Heat conducting fluid; Finite amplitude stability; Thermodynamically open system
• ISSN: 0378-4754; 1872-7166
• DOI: 10.1016/j.matcom.2020.05.009

We investigate finite amplitude stability of spatially inhomogeneous steady state of an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at spatially non-uniform temperature. For a wide class of incompressible viscoelastic models including the Oldroyd-B model, the Giesekus model, the FENE-P model, the Johnson–Segalman model, and the Phan–Thien–Tanner model we prove that the steady state is stable subject to any finite perturbation.