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

10.20347/WIAS.PREPRINT.3104

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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