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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 𝕋2. 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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Cite

BibTeXRIS
BibTeX
@misc{du2026global,
  title = {{Global existence of weak solutions to a nematic electrolyte model in 2D}},
  author = {Hengrong Du and Fizay-Noah Lee and Gieri Simonett},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.36483},
  eprint = {2609.36483},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.36483},
}
RIS
TY  - UNPB
TI  - Global existence of weak solutions to a nematic electrolyte model in 2D
AU  - Hengrong Du
AU  - Fizay-Noah Lee
AU  - Gieri Simonett
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.36483
UR  - https://arxiv.org/abs/2609.36483
AB  - In this paper, we study a system of partial differential equations modeling the dynamics of nematic electrolytes on a two-dimensional torus 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.
ER  -