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Weak sequential stability for a nonlinear model of nematic electrolytes

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    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
    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
    Subject RIV: BA - General Mathematics
    OBOR OECD: Pure mathematics
    Impact factor: 1.233, year: 2019

    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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