Well-posedness of three-dimensional Damped Cahn-Hilliard-Navier-Stokes Equations
This paper presents a mathematical analysis of the evolution of a mixture of two incompressible, isothermal fluids flowing through a porous medium in a three dimensional bounded domain. The model is governed by a coupled system of convective Brinkman Forchheimer equations and the Cahn Hilliard equat...
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| Main Authors | , , |
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| Format | Journal Article |
| Language | English |
| Published |
17.10.2024
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2410.13731 |
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| Summary: | This paper presents a mathematical analysis of the evolution of a mixture of
two incompressible, isothermal fluids flowing through a porous medium in a
three dimensional bounded domain. The model is governed by a coupled system of
convective Brinkman Forchheimer equations and the Cahn Hilliard equation,
considering a regular potential and non degenerate mobility. We first establish
the existence of a Leray Hopf weak solution for the coupled system when the
absorption exponent r greater than or equal to 1. Additionally, we prove that
every weak solution satisfies the energy equality for greater than 3. This
further leads to the uniqueness of weak solutions in three-dimensional bounded
domains, subject to certain restrictions on the viscosity and the Forchheimer
coefficient in the critical case r=3. Moreover, we provide an alternative
simplified proof for the uniqueness of weak solutions for r greater than or
equal to 3 that holds without imposing any restrictions on viscosity or
Forchheimer coefficient. Similar results are also obtained for the case of
degenerate mobility and singular potential. |
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| DOI: | 10.48550/arxiv.2410.13731 |