Global Existence of the Non-isothermal Poisson-Nernst-Planck-Fourier System

23 Jan 2020  ·  Hsieh Chia-Yu, Lin Tai-Chia, Liu Chun, Liu Pei ·

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. read more

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Analysis of PDEs