자료유형  

 학위논문

Control Number  

0016932150

International Standard Book Number  

9798379718060

Dewey Decimal Classification Number  

510

Main Entry-Personal Name  

Ma, Xiao.

Publication, Distribution, etc. (Imprint  

[S.l.] : Princeton University., 2023

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2023

Physical Description  

1 online resource(233 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

General Note  

Advisor: Ionescu, Alexandru.

Dissertation Note  

Thesis (Ph.D.)--Princeton University, 2023.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약In 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 L2 mass term, combining with an almost cancellation identity of the regular pairing and the Deng-Hani's Feynman diagram analysis.

Subject Added Entry-Topical Term  

Mathematics.

Subject Added Entry-Topical Term  

Statistical physics.

Subject Added Entry-Topical Term  

Applied mathematics.

Index Term-Uncontrolled  

Feynman diagram

Index Term-Uncontrolled  

Wave turbulence

Index Term-Uncontrolled  

Four wave models

Index Term-Uncontrolled  

Wave kinetic theory

Added Entry-Corporate Name  

Princeton University Mathematics

Host Item Entry  

Dissertations Abstracts International. 84-12B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:641191