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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}.
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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