References & Citations
Mathematics > Analysis of PDEs
Title: Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies
(Submitted on 4 Jun 2018 (v1), last revised 20 Nov 2019 (this version, v3))
Abstract: We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions. In contrast to previous works, we study a model with a singular non-local free energy, which controls the $H^{\alpha/2}$-norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.
Submission history
From: Helmut Abels [view email][v1] Mon, 4 Jun 2018 09:49:16 GMT (31kb)
[v2] Tue, 2 Oct 2018 20:44:08 GMT (30kb)
[v3] Wed, 20 Nov 2019 14:33:49 GMT (30kb)
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