arXiv Open Access 2026

Long time dynamics of the Nernst-Planck-Darcy System on $\mathbb{R}^3$

Elie Abdo Joe Germany Mohammad Khalil Hamdan Kifah Kontar

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We study ionic electrodiffusion modeled by the Nernst--Planck equations describing the evolution of $N$ ionic species in a three-dimensional incompressible fluid flowing through a porous medium. We address the long-time dynamics of the resulting system in the three-dimensional whole space $\mathbb{R}^3$. We prove that the $k$-th spatial derivatives of each ionic concentration decays to zero in $L^2$ with a sharp rate of order $t^{-\frac{3}{4}-\frac{k}{2}}$. Moreover, we investigate the behavior of the relative entropy associated with the model and show that it blows up in time with a sharp growth rate of order $\log t$.

Topik & Kata Kunci

math.AP

Penulis (4)

Elie Abdo

Joe Germany

Mohammad Khalil Hamdan

Kifah Kontar

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Abdo, E., Germany, J., Hamdan, M.K., Kontar, K. (2026). Long time dynamics of the Nernst-Planck-Darcy System on $\mathbb{R}^3$. https://arxiv.org/abs/2601.02208

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Tahun Terbit: 2026
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓