Weak–strong uniqueness for heat conducting non-Newtonian incompressible fluids

In this work, we introduce a notion of dissipative weak solution for system describing the evolution heat-conducting incompressible non-Newtonian fluid. This concept is based on balance entropy instead energy and has advantage that it admits weak–strong uniqueness principle, justifying proposed formulation. We provide proof existence solutions finite element approximations, thus obtaining first convergence result numerical scheme full evolutionary including temperature dependent coefficients viscous dissipation terms. Then proceed to prove property by means relative inequality.