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Stochastic Analysis of Active Hydrodynamics

Wang, Yixuan (2022) Stochastic Analysis of Active Hydrodynamics. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Wang, Yixuanyiw119@pitt.eduyiw119
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairWang, Dehuadhwang@pitt.edudhwang
Committee MemberJiang, Huiqianghqjiang@pitt.eduhqjiang
Committee MemberChen, Mingmingchen@pitt.edumingchen
Committee MemberMajumdar,
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


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