Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System
Analysis of PDEs
2020-01-24 v1
Abstract
In this paper, we consider a non-isothermal electrokinetic model, which is derived from the Energetic Variational Approach. The charge transport is described through the Poisson-Nernst-Planck equations with variable temperature, and the heat flux satisfies the Fourier's law. This Poisson-Nernst-Planck-Fourier model satisfies both the first law and second law of thermodynamics as well as the Onsager's reciprocal relations, thus it is thermodynamic-consistent. Finally, we prove the global well-posedness for this model under the smallness assumption of the initial data by the energy method.
Keywords
Cite
@article{arxiv.2001.08393,
title = {Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System},
author = {Chia-Yu Hsieh and Tai-Chia Lin and Chun Liu and Pei Liu},
journal= {arXiv preprint arXiv:2001.08393},
year = {2020}
}