A note on the stochastic Ericksen-Leslie equations for nematic liquid crystals

Zdzisław Brzeźniak; Erika Hausenblas; Paul André Razafimandimby

doi:10.3934/dcdsb.2019106

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2019, Volume 24, Issue 11: 5785-5802. Doi: 10.3934/dcdsb.2019106

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A note on the stochastic Ericksen-Leslie equations for nematic liquid crystals

1.
Department of Mathematics, University of York, Heslington Road, York YO10 5DD, UK
2.
Department of Mathematics and Information Technology, Montanuniversität Leoben, Franz Josef Straẞe 18, 8700 Leoben, Austria
3.
Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria 0002, South Africa, Current Address: Department of Mathematics, University of York, Heslington Road, York YO10 5DD, UK

^* Corresponding author: Paul André Razafimandimby
^* Corresponding author: Paul André Razafimandimby

This article is part of a project that is currently funded by the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 791735 "SELEs". Part of this work was written while P. A. Razafimandimby was at the University of Pretoria; he is grateful to the funding he received from the National Research Foundation South Africa (Grant Numbers 109355 and 112084). He is also grateful to the European Mathematical Society for the EMS-Simons for Africa-Collaborative research grant which enables him to visit Montanuniversität Leoben, Austria

Received: June 30, 2018

Early access: June 2019

Published: August 2019

E. Hausenblas is supported by the FWF-Austrian Science Fund through the Stand-Alone grant number P28010

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In this note we prove the existence and uniqueness of local maximal smooth solution of the stochastic simplified Ericksen-Leslie systems modelling the dynamics of nematic liquid crystals under stochastic perturbations.

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Mathematics Subject Classification: Primary: 60H15, 37L40; Secondary: 35R60.

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