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 -