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DC Field | Value | Language |
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dc.contributor.advisor | Ionescu, Alexandru | |
dc.contributor.author | Ma, Xiao | |
dc.contributor.other | Mathematics Department | |
dc.date.accessioned | 2023-07-06T20:22:46Z | - |
dc.date.available | 2023-07-06T20:22:46Z | - |
dc.date.created | 2023-01-01 | |
dc.date.issued | 2023 | |
dc.identifier.uri | http://arks.princeton.edu/ark:/88435/dsp014q77fv60z | - |
dc.description.abstract | In this thesis, we introduce new techniques for studying the random series expansion of dispersive PDEs. We take a quadratic KdV type and a cubic Klein-Gordon type equation as examples to demonstrate the different techniques in three wave and four wave models. For three wave models, we introduce a counting argument to handle the degeneracy problems of the resonance surface and the loss of derivative problem. For four wave models, we introduce a novel renormalization argument and prove a renormalized Wick theorem. We provide a heuristic argument that this renormalization is able to remove all bad terms from the $L^2$ mass term, combining with an almost cancellation identity of the regular pairing and the Deng-Hani's Feynman diagram analysis \cite{deng2021full}, \cite{deng2023derivation}. | |
dc.format.mimetype | application/pdf | |
dc.language.iso | en | |
dc.publisher | Princeton, NJ : Princeton University | |
dc.subject | Feynman diagram | |
dc.subject | wave turbulence | |
dc.subject.classification | Mathematics | |
dc.title | The wave kinetic theory of three wave and four wave models | |
dc.type | Academic dissertations (Ph.D.) | |
pu.date.classyear | 2023 | |
pu.department | Mathematics | |
Appears in Collections: | Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Ma_princeton_0181D_14512.pdf | 1.09 MB | Adobe PDF | View/Download |
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