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Time-periodic solutions of magnetoelastic systems and embedding of the attractor of 2-dimensional Navier-Stokes equations into Euclidean spaces

Mohebbi, Mahdi (2013) Time-periodic solutions of magnetoelastic systems and embedding of the attractor of 2-dimensional Navier-Stokes equations into Euclidean spaces. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

In this work we address two rather independent problems. The first part is dedicated to the existence of periodic solutions for a magnetoelastic system modeling the interaction of a linear elastic body with a nonlinear dissipation and a magnetic field. The resulting system is a coupled Hyperbolic-Parabolic system of PDE’s.
In the second part, for 2-D Navier-Stokes equations on a C2 bounded domain Ω and a time independent force f, a class of nonlinear homeomorphisms is constructed from the attractor of Navier-Stokes to curves in RN, for sufficiently large N. The construction uses an ε-net on Ω (so does not use the information “near” the boundary) and is more physically perceivable compared to abstract common embeddings.

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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Mohebbi, Mahdimam175@pitt.eduMAM175
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Thesis AdvisorGaldi, Giovanni P.galdi@pitt.eduGALDI
Committee MemberRobertson, Ann M.rbertson@pitt.edu RBERTSON
Committee MemberSlaughter, William S.wss@pitt.edu WSS
Committee MemberWang, Dehuadwang@math.pitt.eduDHWANG
Committee MemberZunino, Paolopaz13@pitt.eduPAZ13
Date: 28 June 2013
Date Type: Publication
Defense Date: 4 April 2012
Approval Date: 28 June 2013
Submission Date: 27 March 2013
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 70
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Mechanical Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Attractors, Dynamic Systems, Navier-Stokes Equations, Magnetoelasticity, Periodic Solutions, Hyperbolic-Parabolic Systems
Date Deposited: 28 Jun 2013 20:15
Last Modified: 15 Nov 2016 14:10
URI: http://d-scholarship.pitt.edu/id/eprint/17956

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