论文标题
在有限域上的Nernst-Planck-Euler系统的全球解决方案
Global solutions to the Nernst-Planck-Euler system on bounded domain
论文作者
论文摘要
我们表明,对流体中的离子电泄殖物进行建模的Nernst-Planck-Euler系统具有全球强的解决方案,用于在两个维度界面中任意大数据。物种的假设是有两个物种或扩散率,如果该物种任意很多,离子价度的绝对值是相同的。特别是,离子的边界条件被允许不均匀。该证明基于能量估计,沿特征线的整合以及椭圆和抛物线方程的规则性理论。
We show that the Nernst-Planck-Euler system, which models ionic electrodiffusion in fluids, has global strong solutions for arbitrarily large data in the two dimensional bounded domains. The assumption on species is either there are two species or the diffusivities and the absolute values of ionic valences are the same if the species are arbitrarily many. In particular, the boundary conditions for the ions are allowed to be inhomogeneous. The proof is based on the energy estimates, integration along the characteristic line and the regularity theory of elliptic and parabolic equations.