Weak solution of a stochastic 2D Ericksen–Leslie model driven by jump noise. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Tachim Medjo, T.
• Is Part Of: Stochastics. Volume 93:Issue 1(2021)
• Page Start: 72
• Page End: 109
• Publication Date: 2021-01-02
• Subjects: Stochastic liquid crystal -- Navier–Stokes -- martingale solutions -- Lévy noise -- weak solutions; 35R60 -- 35Q35 -- 60H15 -- 76M35 -- 86A05; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2019.1708363
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : We investigate a stochastic 2D Ericksen–Leslie model with a multiplicative noise of Lévy type. The system models the dynamic of nematic liquid crystals under the influence of stochastic external forces and stretching effects. We prove the existence of a weak martingale solution of the system. The proof of the existence is based on a classical Galerkin approximation as well as some compactness methods. We also prove the pathwise uniqueness of the weak solution when the stretching effect is neglected.