Scattering for the Zakharov System in 3 Dimensions

Zaher Hani; Fabio Pusateri; Jalal Shatah

doi:10.1007/s00220-013-1738-6

Scattering for the Zakharov System in 3 Dimensions

Zaher Hani, Fabio Pusateri, Jalal Shatah

Mathematics

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

Abstract

We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t ^-1, whereas the Schrödinger component decays almost at a rate of t ^-7/6.

Original language	English (US)
Pages (from-to)	731-753
Number of pages	23
Journal	Communications In Mathematical Physics
Volume	322
Issue number	3
DOIs	https://doi.org/10.1007/s00220-013-1738-6
State	Published - Sep 2013

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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title = "Scattering for the Zakharov System in 3 Dimensions",

abstract = "We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t -1, whereas the Schr{\"o}dinger component decays almost at a rate of t -7/6.",

author = "Zaher Hani and Fabio Pusateri and Jalal Shatah",

year = "2013",

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AU - Hani, Zaher

AU - Pusateri, Fabio

AU - Shatah, Jalal

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N2 - We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t -1, whereas the Schrödinger component decays almost at a rate of t -7/6.

AB - We prove global existence and scattering for small localized solutions of the Cauchy problem for the Zakharov system in 3 space dimensions. The wave component is shown to decay pointwise at the optimal rate of t -1, whereas the Schrödinger component decays almost at a rate of t -7/6.

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JO - Communications In Mathematical Physics

JF - Communications In Mathematical Physics

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Scattering for the Zakharov System in 3 Dimensions

Abstract

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