Existence theory for a Poisson-Nernst-Planck model of electrophoresis

Bedin, Luciano; Thompson, Mark

doi:10.3934/cpaa.2013.12.157

Cited by 4 publications

(5 citation statements)

References 28 publications

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“…In terms of the transformed variable ζ from (3.38), the dissipation rate 5) we infer that (4.2) is satisfied. From (4.5) it is now evident that the term − j z j c ∞ j ∇φ ∞ = ∇ j c ∞ j is a gradient field, so also (4.1) is valid.…”

Section: Steady Statesmentioning

confidence: 99%

“…Further in some way related mathematical literature is given by [5,23]. In [5], for instance, motion of a rigid charged macro-molecule immersed in an incompressible ionized fluid is considered and local existence of a weak solution is proved.…”

Section: Introductionmentioning

confidence: 99%

“…In [5], for instance, motion of a rigid charged macro-molecule immersed in an incompressible ionized fluid is considered and local existence of a weak solution is proved. The work [23] deals with a two carriers (anions and cations) electrophoretic model in the whole space R n .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Well-Posedness and Stability of Electrokinetic Flows

Bothe¹,

Fischer²,

Saal³

2014

SIAM J. Math. Anal.

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Abstract. We consider a coupled system of Navier-Stokes and NernstPlanck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the field of micro-and nanofluidics, we consider the model in such generality that electrokinetic flows are included. This prohibits employing the assumption of electroneutrality of the total solution, which is a common approach in the mathematical literature in order to determine the electrical potential. Therefore we complement the system of mass and momentum balances with a Poisson equation for the electrostatic potential, with the charge density stemming from the concentrations of the ionic species. For the resulting Navier-Stokes-Nernst-Planck-Poisson system we prove the existence of unique local strong solutions in bounded domains in R n for any n ≥ 2 as well as the existence of unique global strong solutions and exponential convergence to uniquely determined steady states in two dimensions.

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Section: Steady Statesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Global Well-Posedness and Stability of Electrokinetic Flows

Bothe¹,

Fischer²,

Saal³

2014

SIAM J. Math. Anal.

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“…Lemma 2.2. [37, Lemma 1] Let D be a smooth bounded domain, for any p ∈ [2,4], there exist constants C 1 , C 2 such that…”

Section: Preliminariesmentioning

confidence: 99%

“…To both blocking and selective boundary conditions for the ionic concentrations, [16] proved the global existence in 2d, in the case of uniform selective boundary conditions, the solution was proved unconditional global stability, which converged to unique selected Boltzmann states. For more publications, we refer the readers to [2,17,34,35,40] which dealt with different physical boundary situations and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Well-posedness for the stochastic electrokinetic flow

Qiu¹,

Wang²

2021

Preprint

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We consider the stochastic electrokinetic flow in a smooth bounded domain D, modelled by a Nernst-Planck-Navier-Stokes system with a blocking boundary conditions for ionic species concentrations, perturbed by multiplicative noise. Several results are established in this paper. In both 2d and 3d cases, we establish the global existence of weak martingale solution which is weak in both PDEs and probability sense, and also the existence and uniqueness of the maximal strong pathwise solution which is strong in PDEs and probability sense. Particularly, we show that the maximal pathwise solution is global one in 2d case without the restriction of smallness of initial data.

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Existence and uniqueness of a global weak solution of a Darcy‐Nernst‐Planck‐Poisson system

2012

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This paper deals with the analytical investigations of a nonstationary Darcy‐Nernst‐Planck‐Poisson‐type system which is a mathematical model describing electrolyte solutions. For this nonlinear fully coupled system of partial differential equations we proof existence and uniqueness of global weak solutions. Furthermore, we establish physical properties for the number densities such as nonnegativity and boundedness in L∞((0, T) × Ω) (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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Existence theory for a Poisson-Nernst-Planck model of electrophoresis

Cited by 4 publications

References 28 publications

Global Well-Posedness and Stability of Electrokinetic Flows

Global Well-Posedness and Stability of Electrokinetic Flows

Well-posedness for the stochastic electrokinetic flow

Existence and uniqueness of a global weak solution of a Darcy‐Nernst‐Planck‐Poisson system

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