Global weak solution of the diffusive Johnson-Segalman model of a viscoelastic heat-conducting fluid
| Type of publication: | Misc |
| Citation: | |
| Publication status: | Submitted |
| Year: | 2021 |
| Abstract: | We prove that there exists a~large-data and global-in-time weak solution to a~system of partial differential equations describing an 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 get around the notorious ill-posedness of the diffusive Oldroyd-B model in 3D, 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 and thermodynamical laws. The only real simplification of the model, apart from the incompressibility, homogeneity and isotropicity of the fluid, is that we assume a~linear relation between the temperature and the internal energy. The concept of our weak solution is considerably general as the thermal evolution of the system is governed only by the entropy inequality and the global conservation of energy. Still, this is sufficient for the weak-strong compatibility of our solution and we also specify additional conditions on the material coefficients under which the balances of the total and internal energy hold locally. |
| Preprint project: | NCMM |
| Preprint year: | 2021 |
| Preprint number: | 01 |
| Preprint ID: | NCMM/2021/01 |
| Keywords: | Johnson-Segalman, viscoelastic heat-conducting fluids, weak solution |
| Authors | |
| Added by: | [MB] |
| Total mark: | 0 |
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