Consequences of the choice of a particular basis of L2(S 3) for the cubic wave equation on the sphere and the euclidean space

Anne Sophie De Suzzoni

doi:10.3934/cpaa.2014.13.991

Consequences of the choice of a particular basis of L²(S ³) for the cubic wave equation on the sphere and the euclidean space

Anne Sophie De Suzzoni

CY Cergy Paris Université

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

13 Citations (Scopus)

Résumé

In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low regularity spaces. The result is first proved on the 3D sphere, thanks to the existence of a uniformly bounded in L^p basis of L2(S³) and then it is extended to ℝ³ thanks to the Penrose transform.

langue originale	Anglais
Pages (de - à)	991-1015
Nombre de pages	25
journal	Communications on Pure and Applied Analysis
Volume	13
Numéro de publication	3
Les DOIs	https://doi.org/10.3934/cpaa.2014.13.991
état	Publié - 1 mai 2014
Modification externe	Oui

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10.3934/cpaa.2014.13.991

Contient cette citation

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title = "Consequences of the choice of a particular basis of L2(S 3) for the cubic wave equation on the sphere and the euclidean space",

abstract = "In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low regularity spaces. The result is first proved on the 3D sphere, thanks to the existence of a uniformly bounded in Lp basis of L2(S3) and then it is extended to ℝ3 thanks to the Penrose transform.",

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AU - De Suzzoni, Anne Sophie

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N2 - In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low regularity spaces. The result is first proved on the 3D sphere, thanks to the existence of a uniformly bounded in Lp basis of L2(S3) and then it is extended to ℝ3 thanks to the Penrose transform.

AB - In this paper, the almost sure global well-posedness of the cubic non linear wave equation on the sphere is studied when the initial datum is a random variable with values in low regularity spaces. The result is first proved on the 3D sphere, thanks to the existence of a uniformly bounded in Lp basis of L2(S3) and then it is extended to ℝ3 thanks to the Penrose transform.

KW - Penrose transform

KW - Random initial data

KW - Wave equation

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DO - 10.3934/cpaa.2014.13.991

M3 - Article

AN - SCOPUS:84897800988

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SP - 991

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JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 3

ER -

Consequences of the choice of a particular basis of L2(S 3) for the cubic wave equation on the sphere and the euclidean space

Résumé

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Contient cette citation

Consequences of the choice of a particular basis of L²(S ³) for the cubic wave equation on the sphere and the euclidean space