Martingale solutions of Nematic Liquid Crystals driven by Pure Jump Noise in the Marcus Canonical Form

Akash Panda, Utpal Manna, Zdzislaw Brzezniak

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9 Citations (Scopus)

Abstract

In this work we consider a stochastic evolution equation which describes the system governing the nematic liquid crystals driven by a pure jump noise in the Marcus canonical form. The existence of a martingale solution is proved for both 2D and 3D cases. The construction of the solution relies on a modified Faedo–Galerkin method based on the Littlewood–Paley-decomposition, compactness method and the Jakubowski version of the Skorokhod representation theorem for non-metric spaces. We prove that in the 2-D case the martingale solution is pathwise unique and hence deduce the existence of a strong solution.
Original languageEnglish
Pages (from-to)6204--6283
Number of pages80
Journal Journal of differential equations
Volume266
Issue number10
DOIs
Publication statusPublished - 5 May 2019

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