论文标题
Nernst-Planck-Navier-Stokes Systems远非平衡
Nernst-Planck-Navier-Stokes Systems Far From Equilibrium
论文作者
论文摘要
我们考虑了由Nernst-Planck-Navier-Stokes System描述的流体中的离子电渗作。我们证明，该系统具有用于任意平滑数据的全局平滑解决方案：离子浓度的任意正迪奇特边界条件，潜在的任意dirichlet边界条件，任意的正初始浓度和任意的常规无差初始速度。在两个离子物种的情况下，在三个空间尺寸的有界边界的有界域中，离子的任何正扩散率都具有任何正扩散，并与流体的Stokes方程耦合。如果速度是常规的，则结果也可以保持在Navier-Stokes耦合的情况下。如果它们所有的扩散率相同，则解决方案的全球平滑度对于任意许多离子物种也是如此。
We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. The result holds for any positive diffusivities of ions, in bounded domains with smooth boundary in three space dimensions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier-Stokes coupling, if the velocity is regular. The global smoothness of solutions is also true for arbitrarily many ionic species, if all their diffusivities are the same.
