论文标题
Nernst-Planck-Navier-Stokes Systems的非平衡稳态的存在和稳定性
Existence and Stability of Nonequilibrium Steady States of Nernst-Planck-Navier-Stokes Systems
论文作者
论文摘要
我们考虑在$ {\ mathbb {r}}}^d $的有限域中的Nernst-Planck-navier-Stokes系统，$ d = 2,3 $，带有一般的nonquilibrium dirichlet dirichlet dirichlet dirichlet边界条件。我们证明了平滑稳态解决方案的存在，并仅根据保证这些溶液具有非零流体速度的边界数据提供了足够的条件。我们表明，时间不断发展的解决方案最终是统一的，独立于它们的初始大小。此外，我们考虑一个具有稳定非零电流的维度稳态，并表明它们在三维周期性带中作为解决方案在全球范围内稳定，如果电流足够弱。
We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of ${\mathbb {R}}^d$, $d=2,3$ with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that time evolving solutions are ultimately bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak.
