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

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

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 L^p basis of L2(S³) and then it is extended to ℝ³ thanks to the Penrose transform.

Original language	English
Pages (from-to)	991-1015
Number of pages	25
Journal	Communications on Pure and Applied Analysis
Volume	13
Issue number	3
DOIs	https://doi.org/10.3934/cpaa.2014.13.991
Publication status	Published - 1 May 2014
Externally published	Yes

Keywords

Penrose transform
Random initial data
Wave equation

Access to Document

10.3934/cpaa.2014.13.991

Cite this

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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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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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