TY - JOUR

T1 - Martingale solutions of Nematic Liquid Crystals driven by Pure Jump Noise in the Marcus Canonical Form

AU - Panda, Akash

AU - Manna, Utpal

AU - Brzezniak, Zdzislaw

PY - 2019/5/5

Y1 - 2019/5/5

N2 - 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.

AB - 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.

U2 - https://doi.org/10.1016/j.jde.2018.11.001

DO - https://doi.org/10.1016/j.jde.2018.11.001

M3 - Article

VL - 266

SP - 6204

EP - 6283

JO - Journal of differential equations

JF - Journal of differential equations

IS - 10

ER -