English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We prove the existence of large-data global-in-time weak solutions to anevolutionary PDE system describing flows of incompressible\emph{heat-conducting} viscoelastic rate-type fluids with stress-diffusion,subject to a stick-slip boundary condition for the velocity and a homogeneousNeumann boundary condition for the extra stress tensor. In the introductorysection we develop the thermodynamic foundations of the proposed model, and wedocument the role of thermodynamics in obtaining critical structural relationsbetween the quantities of interest. These structural relations are thenexploited in the mathematical analysis of the governing equations. Inparticular, the definition of weak solution is motivated by the thermodynamicbasis of the model.  The extra stress tensor describing the elastic response of the fluid is inour case purely spherical, which is a simplification from the physical point ofview. The model nevertheless exhibits features that require novel mathematicalideas in order to deal with the technically complex structure of the associatedinternal energy and the more complicated forms of the corresponding entropy andenergy fluxes. The paper provides the first rigorous proof of the existence oflarge-data global-in-time weak solutions to the governing equations for\emph{coupled thermo-mechanical processes} in viscoelastic rate-type fluids.

On incompressible heat-conducting viscoelastic rate-type fluids with stress-diffusion and purely spherical elastic response