Weak sequential stability for a nonlinear model of nematic electrolytes

0537016 - MÚ 2022 RIV US eng J - Journal Article
Feireisl, Eduard - Rocca, E. - Schimperna, G. - Zarnescu, A.
Weak sequential stability for a nonlinear model of nematic electrolytes.
Discrete and Continuous Dynamical systems - Series S. Roč. 14, č. 1 (2021), s. 219-241. ISSN 1937-1632. E-ISSN 1937-1179
R&D Projects: GA ČR(CZ) GA18-05974S
Institutional support: RVO:67985840
Keywords : Nernst-Planck equation * Navier-Stokes system * a-priori estimates * compactness * weak-sequential stability
OECD category: Pure mathematics
Impact factor: 1.865, year: 2021
Method of publishing: Open access
http://dx.doi.org/10.3934/dcdss.2020366

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.
Permanent Link: http://hdl.handle.net/11104/0314773