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arXiv · 1907.03480

Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case

Aaron Brunk·Maria Lukacova-Medvidova
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Abstract

We prove the existence of weak solutions to a viscoelastic phase separation problem in two space dimensions. The mathematical model consists of a Cahn-Hilliard-type equation for two-phase flows and the Peterlin-Navier-Stokes equations for viscoelastic fluids. We focus on the case of a polynomial-like potential and suitably bounded coefficient functions. Using the Lagrange-Galerkin finite element method complex behavior of solution for spinodal decomposition including transient polymeric network structures is demonstrated.

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Aaron Brunk, Maria Lukacova-Medvidova. 2019-07-08. Global existence of weak solutions to viscoelastic phase separation: Part I Regular Case. https://doi.org/10.1088/1361-6544/ac5920

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