Stability of Weak Electrokinetic Flow
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909451058937856 |
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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 |