Global solutions to the Nernst-Planck-Euler system on bounded domain
Analysis of PDEs
2022-12-27 v1
Abstract
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.
Cite
@article{arxiv.2212.12761,
title = {Global solutions to the Nernst-Planck-Euler system on bounded domain},
author = {Dapeng Du and Jingyu Li and Yansheng Ma and Ruyi Pang},
journal= {arXiv preprint arXiv:2212.12761},
year = {2022}
}