Relative energy and weak-strong uniqueness of the two-phase viscoelastic phase separation model

2021/04/01 by Aaron Brunk, Brunk, Aaron, Mária Lukáčová-Medviďová +1 · 1 citation
Computer Science · Mathematics · Engineering · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Composite Material Mechanics

paper · pdf · doi:10.48550/arxiv.2104.00589

Abstract

The aim of this paper is to analyze a viscoelastic phase separation model. We derive a suitable notion of the relative energy taking into account the non-convex nature of the energy law for the viscoelastic phase separation. This allows us to prove the weak-strong uniqueness principle. We will provide the estimates for the full model in two space dimensions. For a reduced model we present the estimates in three space dimensions and derive conditional relative energy estimates.

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• Well-posedness and relaxation in a simplified model for viscoelastic phase separation via Hilbertian gradient flows

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