Abstract/Details

Well -posedness theory of a one parameter family of coupled KdV-type systems and their invariant Gibbs measures


2007 2007

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Abstract (summary)

This thesis concentrates on the study of a conserved Hamiltonian system of nonlinear dispersive partial differential equations. The system consists of two equations of Korteweg-de Vries (KdV) type called the Reduced Equations for Equatorial Baroclinic Barotropic Waves. It was proposed by Majda and Biello as a model to study the nonlinear resonant interaction of barotropic Rossby waves and baroclinic Rossby waves in atmospheric sciences.

We first discuss the existence of the local in time solutions of the system in both periodic and non-periodic settings with a varying coupling parameter. In the periodic setting, we use number-theoretic idea to characterize our result. Then, by the use of modified functionals that are closely related to the original functionals preserved under the flow, we show how to iterate the local in time results and prove the existence of the solutions for all time. Lastly, we discuss the existence of the Gibbs measures that are invariant under the flow and use it to prove the existence of the global in time solutions on the statistical ensemble of the initial data.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Gibbs measures, Korteweg-de Vries systems, Well-posedness
Title
Well -posedness theory of a one parameter family of coupled KdV-type systems and their invariant Gibbs measures
Author
Oh, Choonghong (Tadahiro)
Number of pages
299
Publication year
2007
Degree date
2007
School code
0118
Source
DAI-B 68/11, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780549330813
Advisor
Nahmod, Andrea R.
Committee member
Maroudas, Dimitrios; Rey-Bellet, Luc; Staffilani, Gigliola
University/institution
University of Massachusetts Amherst
Department
Mathematics
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
3289268
ProQuest document ID
304838285
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304838285
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