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arXiv · 2109.10636

Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids

Pablo Alexei Gazca-Orozco·Victoria Patel
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Abstract

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 numerical 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.

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Pablo Alexei Gazca-Orozco, Victoria Patel. 2021-09-22. Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids. https://arxiv.org/abs/2109.10636

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