论文标题
内恩斯特克 - 纳维尔 - 斯托克斯系统中的室内电负性
Interior Electroneutrality in Nernst-Planck-Navier-Stokes Systems
论文作者
论文摘要
我们考虑了由Nernst-Planck-Navier-Stokes System描述的流体离子扩散的Debye长度的极限。在离子浓度的渐近稳定的阻塞案例（消失的正常通量）和均匀的选择性（特殊的Dirichlet）边界条件下，我们证明了离子电荷密度$ρ$及时在域内的内部及时收敛到零，以范围内的范围内的范围内（$ε\ 0 $）。对于离子浓度的Dirichlet边界条件的不稳定状态，我们证明了时间均匀的界限和$ε$。我们还考虑了电荷边界条件，为此，我们证明了在任何固定的$ε> 0 $下实现电压$ρ\ to 0 $，以$ l^p $的速度快速快速快速，所有$ 1 \ le p <\ p <\ f <\ infty $。在具有平稳边界的有限域中，具有任意离子扩散率的两个相对电荷的离子物种的结果得出。
We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions for the ionic concentrations, we prove that the ionic charge density $ρ$ converges in time to zero in the interior of the domain, in the limit of vanishing Debye length ($ε\to 0$). For the unstable regime of Dirichlet boundary conditions for the ionic concentrations, we prove bounds that are uniform in time and $ε$. We also consider electroneutral boundary conditions, for which we prove that electroneutrality $ρ\to 0$ is achieved at any fixed $ε> 0$, exponentially fast in time in $L^p$, for all $1\le p<\infty$. The results hold for two oppositely charged ionic species with arbitrary ionic diffusivities, in bounded domains with smooth boundaries.
