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Probabilistic Perspectives on Dispersive Partial Differential Equations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Probabilistic Perspectives on Dispersive Partial Differential Equations./
作者:	Bringmann, Bjoern.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	410 p.
附註:	Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
Contained By:	Dissertations Abstracts International82-12B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28495334
ISBN:	9798505544921

Probabilistic Perspectives on Dispersive Partial Differential Equations.
Bringmann, Bjoern.

Probabilistic Perspectives on Dispersive Partial Differential Equations. - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 410 p.

Source: Dissertations Abstracts International, Volume: 82-12, Section: B.

Thesis (Ph.D.)--University of California, Los Angeles, 2021.

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

This thesis treats nonlinear dispersive equations with random initial data. First, we study the defocusing energy-critical nonlinear wave equation on Euclidean space. We prove that the scattering mechanism, which is well-understood for smooth initial data, is stable under rough and random perturbations. The main ingredients are Bourgain's bush argument, flux estimates, and a wave packet decomposition of the random linear evolution. Second, we study the three-dimensional wave equation with a Hartree nonlinearity. The main theorem proves the existence and invariance of the Gibbs measure. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. The argument combines techniques from several areas of mathematics, such as dispersive equations, harmonic analysis, and random matrix theory.

ISBN: 9798505544921Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Probability theory

Probabilistic Perspectives on Dispersive Partial Differential Equations.
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300 $a 410 p.
500 $a Source: Dissertations Abstracts International, Volume: 82-12, Section: B.
500 $a Advisor: Tao, Terence Chi-Shen.
502 $a Thesis (Ph.D.)--University of California, Los Angeles, 2021.
506 $a This item must not be sold to any third party vendors.
520 $a This thesis treats nonlinear dispersive equations with random initial data. First, we study the defocusing energy-critical nonlinear wave equation on Euclidean space. We prove that the scattering mechanism, which is well-understood for smooth initial data, is stable under rough and random perturbations. The main ingredients are Bourgain's bush argument, flux estimates, and a wave packet decomposition of the random linear evolution. Second, we study the three-dimensional wave equation with a Hartree nonlinearity. The main theorem proves the existence and invariance of the Gibbs measure. The novelty lies in the singularity of the Gibbs measure with respect to the Gaussian free field. The argument combines techniques from several areas of mathematics, such as dispersive equations, harmonic analysis, and random matrix theory.
590 $a School code: 0031.
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
653 $a Probability theory
653 $a Wave equations
653 $a Nonlinear
653 $a Random initial data
653 $a Defocusing energy-critical
653 $a Euclidean space
653 $a Scattering
653 $a Rough and random perturbations
653 $a Bourgain's bush argument
653 $a Flux estimates
653 $a Wave packets
653 $a Hartree nonlinearity
653 $a Gibbs measure
653 $a Gaussian free field
653 $a Harmonic analysis
653 $a Random matrix theory
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690 $a 0642
710 2 $a University of California, Los Angeles. $b Mathematics 0540. $3 2096468
773 0 $t Dissertations Abstracts International $g 82-12B.
790 $a 0031
791 $a Ph.D.
792 $a 2021
793 $a English
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