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Abels, Helmut ; Weber, Josef

Local well-posedness of a quasi-incompressible two-phase flow

Abels, Helmut and Weber, Josef (2020) Local well-posedness of a quasi-incompressible two-phase flow. Journal of Evolution Equations.

Date of publication of this fulltext: 02 Feb 2021 14:43
Article
DOI to cite this document: 10.5283/epub.44668


Abstract

We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier-Stokes type equation. We prove existence of strong solutions locally ...

We show well-posedness of a diffuse interface model for a two-phase flow of two viscous incompressible fluids with different densities locally in time. The model leads to an inhomogeneous Navier-Stokes/Cahn-Hilliard system with a solenoidal velocity field for the mixture, but a variable density of the fluid mixture in the Navier-Stokes type equation. We prove existence of strong solutions locally in time with the aid of a suitable linearization and a contraction mapping argument. To this end, we show maximal L-2-regularity for the Stokes part of the linearized system and use maximal L-p-regularity for the linearized Cahn-Hilliard system.



Involved Institutions


Details

Item typeArticle
Journal or Publication TitleJournal of Evolution Equations
Publisher:SPRINGER BASEL AG
Open Access Type:DEAL (Springer)
Place of Publication:BASEL
Date12 November 2020
InstitutionsMathematics > Prof. Dr. Helmut Abels
Identification Number
ValueType
10.1007/s00028-020-00646-2DOI
Classification
NotationType
76T99-35Q30-35Q35-76D03-76D05-76D27-76D45MSC
KeywordsDIFFUSE INTERFACE MODEL; WEAK SOLUTIONS; EXISTENCE; FLUIDS; Two-phase flow; Navier-Stokes equation; Diffuse interface model; Mixtures of viscous fluids; Cahn-Hilliard equation
Dewey Decimal Classification500 Science > 510 Mathematics
StatusPublished
RefereedUnknown
Created at the University of RegensburgYes
URN of the UB Regensburgurn:nbn:de:bvb:355-epub-446683
Item ID44668

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