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arXiv · 2609.36483

Global existence of weak solutions to a nematic electrolyte model in 2D

Hengrong Du·Fizay-Noah Lee·Gieri Simonett
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Abstract

In this paper, we study a system of partial differential equations modeling the dynamics of nematic electrolytes on a two-dimensional torus $\mathbb{T}^2$. The model couples the Poisson--Nernst--Planck equations for the evolution of ion concentrations and electrostatic potential with the Ericksen-Leslie equations for the flow and orientation of nematic liquid crystals. We prove the global existence of weak solutions to this system. The proof relies on a Ginzburg-Landau approximation scheme. Key steps include deriving uniform energy estimates and establishing the strong convergence of the director field by utilizing a Pohozaev-type identity to handle the lack of compactness in the Ericksen stress tensor.

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Hengrong Du, Fizay-Noah Lee, Gieri Simonett. 2026-09-29. Global existence of weak solutions to a nematic electrolyte model in 2D. https://arxiv.org/abs/2609.36483

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