{Some Analytical Issues for the Selected Complex Fluids Models

Yu, Cheng (2013) {Some Analytical Issues for the Selected Complex Fluids Models. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

In this dissertation, we study the selected models from complex fluids: compressible flow of liquid crystals and the incompressible fluid-particles flow. On the compressible flow of liquid crystals, we establish the global existence of renormalized weak solutions when $\gamma>\frac{3}{2}$ through a three-level approximation, energy estimates, and weak
convergence methods in the spirit of the so-called Lions-Feireisl method. On the incompressible fluid-particles flow, we establish the global existence of Leray weak solutions which was constructed by the Galerkin methods, fixed point arguments, and convergence analysis with the large initial data. The uniqueness was established by the classical theory of Stokes equations and a bootstrap argument in the two dimensional space.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Yu, Cheng chy39@pitt.edu CHY39
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Wang, Dehua dwang@math.pitt.edu DHWANG Committee Member Galdi, Giovanni galdi@pitt.edu GALDI Committee Member Marta, Lewicka LEWICKA@pitt.edu LEWICKA Committee Member Huijiang, Jiang hqjiang@math.pitt.edu HQJIANG Committee Member Noel, Walkington noelw@andrew.cmu.edu
Date:	18 October 2013
Date Type:	Publication
Defense Date:	1 April 2013
Approval Date:	18 October 2013
Submission Date:	24 July 2013
Access Restriction:	2 year -- Restrict access to University of Pittsburgh for a period of 2 years.
Number of Pages:	97
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:	Global weak solutions, existence, uniqueness, liquid crystal, Navier-Stokes equations, Vlasov equation
Date Deposited:	18 Oct 2013 14:53
Last Modified:	15 Nov 2016 14:14
URI:	http://d-scholarship.pitt.edu/id/eprint/19458

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