Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids
Gazca Orozco PA, Patel V (2024)
Publication Language: English
Publication Status: In review
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
Publisher: Nonlinear Analysis: Real World Applications
DOI: 10.1016/j.nonrwa.2022.103664
Open Access Link: https://arxiv.org/abs/2109.10636
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.
Authors with CRIS profile
Pablo Alexei Gazca Orozco
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
United Kingdom (GB)How to cite
APA:
Gazca Orozco, P.A., & Patel, V. (2024). Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids. (Unpublished, In review).
MLA:
Gazca Orozco, Pablo Alexei, and Victoria Patel. Weak-strong Uniqueness for Heat Conducting non-Newtonian Incompressible Fluids. Unpublished, In review. 2024.
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