Stability of Weak Electrokinetic Flow

Fuente: arXiv
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Auteur principal: Lee, Fizay-Noah
Format: Preprint
Publié: 2025
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author Lee, Fizay-Noah
author_facet Lee, Fizay-Noah
contents We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium steady state solutions of the system, characterized by zero fluid flow, are asymptotically stable. In these regimes, the existence of a natural dissipative structure is critical in obtaining stability. This structure, in general, breaks down under nonequilibrium conditions, in which case, in the steady state, the fluid flow may be nontrivial. In this short paper, we show that, nonetheless, certain classes of very weak nonequilibrium steady states, with nonzero fluid flow, remain globally asymptotically stable.
format Preprint
id arxiv_https___arxiv_org_abs_2501_04152
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stability of Weak Electrokinetic Flow
Lee, Fizay-Noah
Analysis of PDEs
35Q30, 35Q35, 35Q92
We consider the Nernst-Planck-Stokes system on a bounded domain of $\mathbb{R}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. It is well known that, in a wide range of cases, equilibrium steady state solutions of the system, characterized by zero fluid flow, are asymptotically stable. In these regimes, the existence of a natural dissipative structure is critical in obtaining stability. This structure, in general, breaks down under nonequilibrium conditions, in which case, in the steady state, the fluid flow may be nontrivial. In this short paper, we show that, nonetheless, certain classes of very weak nonequilibrium steady states, with nonzero fluid flow, remain globally asymptotically stable.
title Stability of Weak Electrokinetic Flow
topic Analysis of PDEs
35Q30, 35Q35, 35Q92
url https://arxiv.org/abs/2501.04152