Weak–strong uniqueness for heat conducting non-Newtonian incompressible fluids. (December 2022)

• Record Type: Journal Article
• Authors: Gazca-Orozco, Pablo Alexei; Patel, Victoria
• Is Part Of: Nonlinear analysis. Volume 68(2022)
• Publication Date: 2022-12
• Subjects: Non-Newtonian fluid -- Heat-conducting fluid -- Weak–strong uniqueness -- Finite element method; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103664
• Languages: English
• ISSNs: 1468-1218

Abstract

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.