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Global Well-Posedness of Stochastic Nematic Liquid Crystals with Random Initial and Boundary Conditions Driven by Multiplicative Noise
,
Jiang-lun Wu
Applied Mathematics & Optimization, Volume: 87, Issue: 1, Pages: 1 - 46
Swansea University Author:
Jiang-lun Wu
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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...
| Published in: | Applied Mathematics & Optimization |
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| ISSN: | 0095-4616 1432-0606 |
| Published: |
Switzerland AG
Springer Science and Business Media LLC
2023
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa60862 |
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| 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 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. |
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| Keywords: |
Stochastic nematic liquid crystals flows; Anticipating initial condition; Malliavin derivative; Apriori estimates; Skorohod integral |
| College: |
Faculty of Science and Engineering |
| Funders: |
NNSF of China(Grant No. 11971077, 11801283), Chongqing Key Laboratory of
Analytic Mathematics and Applications, Chongqing University, Chongqing, 401331,China. |
| Issue: |
1 |
| Start Page: |
1 |
| End Page: |
46 |