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Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise

Lidan Wang, Guoli Zhou Orcid Logo, Jiang-lun Wu Orcid Logo

Applied Mathematics & Optimization, Volume: 87, Issue: 1, Pages: 1 - 46

Swansea University Author: Jiang-lun Wu Orcid Logo

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DOI (Published version): 10.1007/s00245-022-09909-5

Abstract

The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamicalmodel, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In this article, we consider a 2-D stochastic nematic liquid cryst...

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Published in: Applied Mathematics & Optimization
ISSN: 0095-4616 1432-0606
Published: Switzerland AG Springer Science and Business Media LLC 2023
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URI: https://cronfa.swan.ac.uk/Record/cronfa60862
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first_indexed 2022-08-21T20:13:08Z
last_indexed 2023-03-02T04:15:02Z
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spelling 2023-03-01T12:23:15.9459271 v2 60862 2022-08-21 Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise dbd67e30d59b0f32592b15b5705af885 0000-0003-4568-7013 Jiang-lun Wu Jiang-lun Wu true false 2022-08-21 SMA The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamicalmodel, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In this article, we consider a 2-D stochastic nematic liquid crystals with the velocity field perturbed by affine-linear multiplicative white noise, with random initial data and random boundary conditions. Our main objective is to obtain the global well-posedness of the stochastic equations under the sufficient Malliavin regularity of the initial condition. The Malliavin calculus techniques play important roles when we obtain the global existence of the solutions to the stochastic nematic liquid crystal model with random initial and boundary conditions. Journal Article Applied Mathematics &amp; Optimization 87 1 1 46 Springer Science and Business Media LLC Switzerland AG 0095-4616 1432-0606 Stochastic nematic liquid crystals flows; Anticipating initial condition; Malliavin derivative; Apriori estimates; Skorohod integral 1 2 2023 2023-02-01 10.1007/s00245-022-09909-5 http://dx.doi.org/10.1007/s00245-022-09909-5 COLLEGE NANME Mathematics COLLEGE CODE SMA Swansea University Other NNSF of China(Grant No. 11971077, 11801283), Chongqing Key Laboratory of Analytic Mathematics and Applications, Chongqing University, Chongqing, 401331,China. 2023-03-01T12:23:15.9459271 2022-08-21T21:01:30.0271306 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Lidan Wang 1 Guoli Zhou 0000-0002-6599-1859 2 Jiang-lun Wu 0000-0003-4568-7013 3 Under embargo Under embargo 2022-08-21T21:12:23.9898377 Output 219862 application/pdf Accepted Manuscript true 2023-11-07T00:00:00.0000000 true eng
title Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
spellingShingle Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
Jiang-lun Wu
title_short Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
title_full Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
title_fullStr Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
title_full_unstemmed Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
title_sort Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
author_id_str_mv dbd67e30d59b0f32592b15b5705af885
author_id_fullname_str_mv dbd67e30d59b0f32592b15b5705af885_***_Jiang-lun Wu
author Jiang-lun Wu
author2 Lidan Wang
Guoli Zhou
Jiang-lun Wu
format Journal article
container_title Applied Mathematics &amp; Optimization
container_volume 87
container_issue 1
container_start_page 1
publishDate 2023
institution Swansea University
issn 0095-4616
1432-0606
doi_str_mv 10.1007/s00245-022-09909-5
publisher Springer Science and Business Media LLC
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
url http://dx.doi.org/10.1007/s00245-022-09909-5
document_store_str 0
active_str 0
description The flow of nematic liquid crystals can be described by a highly nonlinear stochastic hydrodynamicalmodel, thus is often influenced by random fluctuations, such as uncertainty in specifying initial conditions and boundary conditions. In this article, we consider a 2-D stochastic nematic liquid crystals with the velocity field perturbed by affine-linear multiplicative white noise, with random initial data and random boundary conditions. Our main objective is to obtain the global well-posedness of the stochastic equations under the sufficient Malliavin regularity of the initial condition. The Malliavin calculus techniques play important roles when we obtain the global existence of the solutions to the stochastic nematic liquid crystal model with random initial and boundary conditions.
published_date 2023-02-01T04:19:20Z
_version_ 1763754282874568704
score 11.013148

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