Nernst–Planck–Navier–Stokes Systems far from Equilibrium

Constantin, Peter; Ignatova, Mihaela

doi:10.1007/s00205-021-01630-x

Cited by 21 publications

(68 citation statements)

References 14 publications

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“…When the ionic concentrations satisfy either the blocking boundary conditions or the uniformly selective boundary conditions, strong solutions are global in two dimensions [6], and in three dimensions provided that the initial data is a small perturbation of a steady state [8]. If both the ionic concentrations and the electrical potential obey the Dirichlet boundary conditions, global strong solutions exist in three dimensions as long as the fluid velocity is regular [9]. With periodic boundary conditions, two dimensional strong solutions exist globally in time, and long time behaviors of the solutions are studied in [1] under the influence of body forces or body charges.…”

Section: Introductionmentioning

confidence: 99%

“…In the limit of zero viscosity in the Navier-Stokes equations, the solutions of NPNS system in two dimensions converges to the solutions of the corresponding Nernst-Planck-Euler (NPE) system, whose solutions exist and are global [14,25,27]. For the Nernst-Planck system coupled with time dependent Stokes equations, solutions are known existing globally in time in three dimensions [9,17].…”

Section: Introductionmentioning

confidence: 99%

“…It follows from (1.1) that the property (1.7) is preserved in time. For regular solutions of NPNS it is shown in [6,9] that if c i (0) ≥ 0, then c i (x, t) remains nonnegative for t > 0. This property follows from (1.1) if c i are known to be sufficiently regular, and the same proof and result holds for the NPD equations.…”

Section: Introductionmentioning

confidence: 99%

“…The existence of globally smooth solutions of three dimensional Nernst-Planck equations with arbitrary large data coupled to Stokes equations driven by the Lorentz force has been obtained only recently in [9,17]. Replacing viscous dissipation by friction diminishes the regularizing effect by two differential orders.…”

Section: Introductionmentioning

confidence: 99%

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Charged Fluids in Porous Media

Ignatova,

Shu

2021

Preprint

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The Nernst-Planck-Darcy system models ionic electrodiffusion in porous media. We consider the system for two ionic species with opposite valences. We prove that the initial value problem for the Nernst-Planck-Darcy system in periodic domains in two or three dimensions has global weak solutions in W 1,p (p ≥ 2). We obtain furthermore global existence and uniqueness of smooth solutions for arbitrary large data.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Charged Fluids in Porous Media

Ignatova,

Shu

2021

Preprint

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“…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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On the Space Analyticity of the Nernst–Planck–Navier–Stokes system

Abdo

Ignatova

2022

J. Math. Fluid Mech.

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We consider an electrodiffusion model that describes the intricate interplay of multiple ionic species with a twodimensional, incompressible, viscous fluid subjected to stochastic additive noise. This system involves nonlocal nonlinear drift-diffusion Nernst-Planck equations for ionic species and stochastic Navier-Stokes equations for fluid motion under the influence of electric and time-independent forces. Under the selective boundary conditions imposed on the concentrations, we establish the existence and uniqueness of global pathwise solutions to this system on smooth bounded domains. Our study also investigates long-time ionic concentration dynamics and explores Feller properties of the associated Markovian semigroup. In the context of equal diffusive species and under appropriate conditions, we demonstrate the existence of invariant ergodic measures supported on H 2 . We then enhance the ergodicity results on periodic tori and obtain smooth invariant measures under a constraint on the initial spatial averages of the concentrations. The uniqueness of the invariant measures on periodic boxes and smooth bounded domains is further established when the noise forces sufficient modes, and the diffusivities of the species are large. Finally, in the case of two ionic species with equal diffusivities and valences of 1 and −1, we study the rate of convergence of the Markov transition kernels to the invariant measure and obtain unconditional, unique exponential ergodicity for the model.

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Nernst–Planck–Navier–Stokes Systems far from Equilibrium

Cited by 21 publications

References 14 publications

Charged Fluids in Porous Media

Charged Fluids in Porous Media

Well-posedness for the stochastic electrokinetic flow

On the Space Analyticity of the Nernst–Planck–Navier–Stokes system

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