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The Wave Kinetic Theory of Three Wave and Four Wave Models.

Record Type:	Electronic resources : Monograph/item
Title/Author:	The Wave Kinetic Theory of Three Wave and Four Wave Models.
Author:	Ma, Xiao.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2023
Description:	233 p.
Notes:	Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
Notes:	Advisor: Ionescu, Alexandru.
Contained By:	Dissertations Abstracts International84-12B.
Subject:	Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30487908
ISBN:	9798379718060

The Wave Kinetic Theory of Three Wave and Four Wave Models.
Ma, Xiao.

The Wave Kinetic Theory of Three Wave and Four Wave Models. - Ann Arbor : ProQuest Dissertations & Theses, 2023 - 233 p.

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

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

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

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

ISBN: 9798379718060Subjects--Topical Terms:

184409
Mathematics.
Subjects--Index Terms:

Feynman diagram

The Wave Kinetic Theory of Three Wave and Four Wave Models.
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100 1 $a Ma, Xiao. $3 966838
245 1 0 $a The Wave Kinetic Theory of Three Wave and Four Wave Models.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2023
300 $a 233 p.
500 $a Source: Dissertations Abstracts International, Volume: 84-12, Section: B.
500 $a Advisor: Ionescu, Alexandru.
502 $a Thesis (Ph.D.)--Princeton University, 2023.
506 $a This item must not be sold to any third party vendors.
520 $a 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 L2 mass term, combining with an almost cancellation identity of the regular pairing and the Deng-Hani's Feynman diagram analysis.
590 $a School code: 0181.
650 4 $a Mathematics. $3 184409
650 4 $a Statistical physics. $3 183716
650 4 $a Applied mathematics. $3 377601
653 $a Feynman diagram
653 $a Wave turbulence
653 $a Four wave models
653 $a Wave kinetic theory
690 $a 0405
690 $a 0217
690 $a 0364
710 2 $a Princeton University. $b Mathematics. $3 966839
773 0 $t Dissertations Abstracts International $g 84-12B.
790 $a 0181
791 $a Ph.D.
792 $a 2023
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30487908