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Zbl 1229.35215
Schmuck, Markus
Analysis of the Navier-Stokes-Nernst-Planck-Poisson system. (English)
[J] Math. Models Methods Appl. Sci. 19, No. 6, 993-1015 (2009). ISSN 0218-2025

Summary: We study a fluid-dynamical model based on a coupled Navier-Stokes-Nernst-Planck-Poisson system. Of special interest are the fluid velocity, concentrations of charged particles ranging from colloidal to nano size and the induced quasi-electrostatic potential, which all depend on an externally applied electrical field. For $d\le 3$ we prove existence, and in some cases uniqueness of weak solutions. Moreover we characterize solutions via energy laws, mass conservation, non-negativity and pointwise bounds. Further the system enjoys an entropy law. Existence of locally strong solutions is verified.

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
76W05 Flows in presence of electromagnetic forces
74F10 Fluid-solid interactions
52C45 Combinatorial complexity of geometric structures

Keywords: Navier-Stokes-Nernst-Planck-Poisson system; solid-liquid interface; electrorheological behavior

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