Coupling the Navier–Stokes–Fourier equations with the Johnson–Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis

Michal Bathory, Miroslav Bulíček (Korresp. Autor*in), Josef Málek

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed


We prove that there exists a large-data and global-in-time weak solution to a system of partial differential equations describing the unsteady flow of an incompressible heat-conducting rate-type viscoelastic stress-diffusive fluid filling up a mechanically and thermally isolated container of any dimension. To overcome the principal difficulties connected with ill-posedness of the diffusive Oldroyd-B model in three dimensions, we assume that the fluid admits a strengthened dissipation mechanism, at least for excessive elastic deformations. All the relevant material coefficients are allowed to depend continuously on the temperature, whose evolution is captured by a thermodynamically consistent equation. In fact, the studied model is derived from scratch using only the balance equations for linear momentum and energy, the formulation of the second law of thermodynamics and the constitutive equation for the internal energy. The latter is assumed to be a linear function of temperature, which simplifies the model. The concept of our weak solution incorporates both the temperature and entropy inequalities, and also the local balance of total energy provided that the pressure function exists.
Seiten (von - bis)417-476
FachzeitschriftMathematical Models and Methods in Applied Sciences
PublikationsstatusVeröffentlicht - 19 Jan. 2024

ÖFOS 2012

  • 103032 Strömungslehre
  • 101002 Analysis
  • 101028 Mathematische Modellierung