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

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Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise. / Brzezniak, Zdzislaw; Hausenblas, Erika; Razafimandimby, Paul André.
In: Indiana University mathematics journal, Vol. 70.2021, No. 5, 2021, p. 2177-2235.

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@article{b5920329611540d698d58a6b2a5e97a7,
title = "Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise",
abstract = "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 evolutionequations with coefficients satisfying local Lipschitz condition involving the norms of two differentBanach spaces.",
author = "Zdzislaw Brzezniak and Erika Hausenblas and Razafimandimby, {Paul Andr{\'e}}",
year = "2021",
doi = "10.1512/iumj.2021.70.8678",
language = "English",
volume = "70.2021",
pages = "2177--2235",
journal = "Indiana University mathematics journal",
issn = "0022-2518",
number = "5",

}

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TY - JOUR

T1 - Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise

AU - Brzezniak, Zdzislaw

AU - Hausenblas, Erika

AU - Razafimandimby, Paul André

PY - 2021

Y1 - 2021

N2 - 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 evolutionequations with coefficients satisfying local Lipschitz condition involving the norms of two differentBanach spaces.

AB - 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 evolutionequations with coefficients satisfying local Lipschitz condition involving the norms of two differentBanach spaces.

U2 - 10.1512/iumj.2021.70.8678

DO - 10.1512/iumj.2021.70.8678

M3 - Article

VL - 70.2021

SP - 2177

EP - 2235

JO - Indiana University mathematics journal

JF - Indiana University mathematics journal

SN - 0022-2518

IS - 5

ER -