Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise

Zdzislaw Brzezniak, Erika Hausenblas, Paul André Razafimandimby

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In this paper, we prove the existence of a unique maximal local strong solutions to a stochastic system for both 2D and 3D penalised nematic liquid crystals driven by multiplicative Gaussian noise. In the 2D case, we show that this solution is global. As a by-product of our investigation, but of independent interest, we present a general method based on fixed point arguments to establish the existence and uniqueness of a maximal local solution of an abstract stochastic evolution
equations with coefficients satisfying local Lipschitz condition involving the norms of two different
Banach spaces.
Original languageEnglish
Pages (from-to)2177-2235
Number of pages41
JournalIndiana University mathematics journal
Issue number5
Publication statusPublished - 2021

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