Wang, Yixuan
(2022)
Stochastic Analysis of Active Hydrodynamics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We study the hydrodynamics of nematic liquid crystal flow perturbed by a multiplicative noise under the Beris-Edwards framework. For the stochastic active liquid crystal system, we built the existence of the weak global martingale solution in a 3-D smooth bounded domain through a four-level approximation scheme. The existence of the limit of approximate solutions in the presence of random variables is guaranteed by the classical Skorokhod representation theorem. For the three-dimensional compressible Navier-Stokes equations coupled with the Q-tensor equation, we first constructed the local existence and uniqueness of strong pathwise solution up to a positive stopping time to the system, then we proved that the local stopping time could be extended to maximal. Note that the construction of the local solution is built upon a cutting-off argument. We also studied the connection between the compressible Navier-Stokes equations coupled by the Q-tensor equation for liquid crystals with the incompressible system in the periodic case. As the Mach number approaches zero, we proved that, both in the deterministic and stochastic case, that the weak solutions of the compressible nematic liquid crystal model would converge to the solution of the incompressible one.
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| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
20 July 2022 |
| Date Type: |
Publication |
| Defense Date: |
5 April 2022 |
| Approval Date: |
20 July 2022 |
| Submission Date: |
6 April 2022 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
154 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Navier-Stokes equations, stochastic active liquid crystal system, stochastic compressible liquid crystal system, weak solution, global martingale solution, local strong pathwise solution, uniqueness, stochastic compactness, Mach number, incompressible limit |
| Date Deposited: |
20 Jul 2022 17:44 |
| Last Modified: |
20 Jul 2022 17:44 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/42501 |
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