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http://arks.princeton.edu/ark:/88435/dsp014q77fv60z
Title: | The wave kinetic theory of three wave and four wave models |
Authors: | Ma, Xiao |
Advisors: | Ionescu, Alexandru |
Contributors: | Mathematics Department |
Keywords: | Feynman diagram wave turbulence |
Subjects: | Mathematics |
Issue Date: | 2023 |
Publisher: | Princeton, NJ : Princeton University |
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}. |
URI: | http://arks.princeton.edu/ark:/88435/dsp014q77fv60z |
Type of Material: | Academic dissertations (Ph.D.) |
Language: | en |
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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