发表机构
School of Mathematics, Nanjing University（南京大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究二维周期性通道中由壁面运动和切向电场驱动的离子流体的电动力学 Couette 态，证明了电中性态在不等扩散系数下的线性与非线性指数稳定性，并构造了 Poisson--Boltzmann/电渗 Couette 族及其稳定性。
AI 中文摘要
本文研究了一个在周期性通道中由壁面运动和施加的切向电场驱动的二维 Poisson--Nernst--Planck--Navier--Stokes 系统，其中包含两种可能具有不等扩散系数的离子物种。在电中性 Couette 态下，扩散系数加权的离子能量与线性化算子的三角结构相结合，对于固定的 \\((A,E_0)\\) 和所有正的扩散系数，可得到指数线性稳定性。随后，通过将解析半群平滑与二次估计相结合，在与生成元的图域相适应的复插值空间上，获得了小数据非线性指数稳定性。对于不等扩散系数，线性化离子子系统的非零流向模态在显式强剪切条件下满足速率为 \\(D_{\min}^{1/3}|A|^{2/3}\\) 的有界通道增强耗散估计。当 \\(D_+=D_-\\) 时，Fourier 模态分解将共同的 Couette 平流--扩散算子与一个收缩的漂移--反应半群分离，因此在没有任何静电耦合小性条件的情况下，保留了相同的标量混合速率。我们还针对指定的壁面电势构造了一个精确的 Poisson--Boltzmann/电渗 Couette 族。对于足够小的壁面电势振幅，其线性化生成元是电中性生成元的小图域扰动，这在同一插值尺度上产生了线性和非线性指数稳定性。
英文摘要
In this paper, we study a two-dimensional Poisson--Nernst--Planck--Navier--Stokes system in a periodic channel driven by wall motion and an imposed tangential electric field, with two ionic species that may have unequal diffusivities. At the electroneutral Couette state, a diffusivity-weighted ionic energy combines with the triangular structure of the linearized operator to yield exponential linear stability for fixed \((A,E_0)\) and all positive diffusivities. Small-data nonlinear exponential stability is then obtained on a complex interpolation space adapted to the graph domain of the generator by combining analytic-semigroup smoothing with quadratic estimates. For unequal diffusivities, the nonzero streamwise modes of the linearized ionic subsystem satisfy a bounded-channel enhanced-dissipation estimate at rate \(D_{\min}^{1/3}|A|^{2/3}\) under an explicit strong-shear condition. When \(D_+=D_-\), a Fourier-mode factorization separates the common Couette advection--diffusion operator from a contractive drift--reaction semigroup, so the same scalar mixing rate is retained without any smallness condition on the electrostatic coupling. We also construct an exact Poisson--Boltzmann/electroosmotic Couette family for prescribed wall potentials. For sufficiently small wall-potential amplitude, its linearized generator is a small graph-domain perturbation of the electroneutral generator, which yields linear and nonlinear exponential stability on the same interpolation scale.
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