Martingale solutions of nematic liquid crystals driven by pure jump noise in the Marcus canonical form

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Brzezniak, Zdzislaw¹  Manna, Utpal²  Panda, Akash Ashirbad² 

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Indian Inst Sci Educ & Res Thiruvananthapuram, Sch Math, Vithura 695551, India

关键词: Nematic liquid crystal;    Martingale solutions;    Marcus canonical form;    Skorokhod representation theorem;   

DOI  :  10.1016/j.jde.2018.11.001

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free