WIAS Preprint No. 3104, (2024)
Existence of weak solutions to an anisotropic electrokinetic flow model
Authors
- Hömberg, Dietmar
ORCID: 0000-0001-9460-5729 - Lasarzik, Robert
ORCID: 0000-0002-1677-6925 - Plato, Luisa
ORCID: 0000-0003-3456-1570
2020 Mathematics Subject Classification
- 35D30 35G61 35Q30
Keywords
- Suitable weak solutions, nonlinear coupled PDEs, anisotropy
DOI
Abstract
In this article we present a system of coupled non-linear PDEs modelling an anisotropic electrokinetic flow. We show the existence of suitable weak solutions in three spatial dimensions, that is weak solutions which fulfill an energy inequality, via a regularized system. The flow is modelled by a Navier--Stokes--Nernst--Planck--Poisson system and the anisotropy is introduced via space dependent diffusion matrices in the Nernst--Planck and Poisson equation.
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