Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids [article]

Pablo Alexei Gazca-Orozco, Victoria Patel
2022 arXiv   pre-print
In this work, we introduce a notion of dissipative weak solution for a system describing the evolution of a heat-conducting incompressible non-Newtonian fluid. This concept of solution is based on the balance of entropy instead of the balance of energy and has the advantage that it admits a weak-strong uniqueness principle, justifying the proposed formulation. We provide a proof of existence of solutions based on finite element approximations, thus obtaining the first convergence result of a
more » ... erical scheme for the full evolutionary system including temperature dependent coefficients and viscous dissipation terms. Then we proceed to prove the weak-strong uniqueness property of the system by means of a relative energy inequality.
arXiv:2109.10636v2 fatcat:ctg6lfc5xjbj5bttcnsblvcpty