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

Gazca Orozco PA, Patel V (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Nonlinear Analysis-Real World Applications Elsevier

Book Volume: 68

DOI: 10.1016/j.nonrwa.2022.103664

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.(C) 2022 Elsevier Ltd. All rights reserved.

Authors with CRIS profile

Pablo Alexei Gazca Orozco Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

University of Oxford

United Kingdom (GB)

How to cite

APA:

Gazca Orozco, P.A., & Patel, V. (2022). Weak-strong uniqueness for heat conducting non-Newtonian incompressible fluids. Nonlinear Analysis-Real World Applications, 68. https://dx.doi.org/10.1016/j.nonrwa.2022.103664

MLA:

Gazca Orozco, Pablo Alexei, and Victoria Patel. "Weak-strong uniqueness for heat conducting non-Newtonian incompressible fluids." Nonlinear Analysis-Real World Applications 68 (2022).

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