论文标题
Nernst-Planck-Navier-Stokes Systems在平衡附近
Nernst-Planck-Navier-Stokes systems near equilibrium
论文作者
论文摘要
Nernst-Planck-navier-Stokes系统模型在流体中的离子电渗作。我们证明了在三个维度中的界面域中的全局溶液存在，其中具有离子浓度的封闭（无液压）或均匀的选择性（特殊的dirichlet）边界条件。对于足够小的稳态解决方案扰动的初始条件，建立了强大解决方案的全球存在。在强规范中，该溶液保持接近平衡。证明的主要两个步骤是（1）相对熵的总和（kullback-leibler Diverences）和（2）通过相对熵的总和对$ l^2 $差异的控制。
The Nernst-Planck-Navier-Stokes system models electrodiffusion of ions in a fluid. We prove global existence of solutions in bounded domains in three dimensions with either blocking (no-flux) or uniform selective (special Dirichlet) boundary conditions for ion concentrations. The global existence of strong solutions is established for initial conditions that are sufficiently small perturbations of steady state solutions. The solutions remain close to equilibrium in strong norms. The main two steps of the proof are (1) the decay of the sum of relative entropies (Kullback-Leibler divergences) and (2) the control of $L^2$ norms of deviations by the sum of relative entropies.
