期刊
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
卷 14, 期 1, 页码 219-241出版社
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdss.2020366
关键词
Nernst-Planck equation; Navier-Stokes system; a-priori estimates; compactness; weak-sequential stability
资金
- GNAMPA (Gruppo Nazionale per l'Analisi Matematica, la Probabilita e le loro Applicazioni) of INdAM (Istituto Nazionale di Alta Matematica)
- Italian Ministry of Education, University and Research (MIUR): Dipartimenti di Eccellenza Program (2018-2022) - Dept. of Mathematics F. Casorati, University of Pavia
- Basque Government through the BERC 2018-2021 program
- Spanish Ministry of Economy and Competitiveness MINECO through BCAM Severo Ochoa excellence accreditation [SEV-2017-0718]
- Spanish Ministry of Economy and Competitiveness MINECO - (AEI/FEDER, UE) [MTM2017-82184-R]
- DESFLU
- Czech Sciences Foundation (GACR) [18-05974S]
- [RVO:67985840]
This article studies a system of nonlinear PDEs modeling the electrokinetics of a nematic electrolyte material consisting of various ion species in a nematic liquid crystal. It focuses on the two-species case and proves apriori estimates providing weak sequential stability, the main step towards proving the existence of weak solutions.
In this article we study a system of nonlinear PDEs modelling the electrokinetics of a nematic electrolyte material consisting of various ions species contained in a nematic liquid crystal. The evolution is described by a system coupling a Nernst-Planck system for the ions concentrations with a Maxwell's equation of electrostatics governing the evolution of the electrostatic potential, a Navier-Stokes equation for the velocity field, and a non-smooth Allen-Cahn type equation for the nematic director field. We focus on the two-species case and prove apriori estimates that provide a weak sequential stability result, the main step towards proving the existence of weak solutions.
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