Strong solution to stochastic penalised nematic liquid crystals model driven by multiplicative Gaussian noise
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In: Indiana University mathematics journal, Vol. 70.2021, No. 5, 2021, p. 2177-2235.
Research output: Contribution to journal › Article › Research › peer-review
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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 -