Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system
Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system
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DOI：
10.1016/j.jde.2020.05.037
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
C. Hsieh;Tai-Chia Lin;Chun Liu;Pei Liu
中科院分区：
文献类型：
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作者：
C. Hsieh;Tai-Chia Lin;Chun Liu;Pei Liu
本文用能量变分法推导了一个非等温电动力学模型。在变温度条件下，电荷输运用泊松-能-普朗克方程描述，热通量满足傅里叶定律。该泊松-能-普朗克-傅立叶模型既满足热力学第一定律和第二定律，又满足昂萨格互反关系，因此是热力学一致的。最后，在初始数据较小的假设下，用能量法证明了该模型的全局适定性。
In this paper, we use the Energetic Variational Approach to derive a non-isothermal electrokinetic model. 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.