### 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 | |

State | Published - Sep 2013 |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*322*(3), 731-753. https://doi.org/10.1007/s00220-013-1738-6

**Scattering for the Zakharov System in 3 Dimensions.** / Hani, Zaher; Pusateri, Fabio; Shatah, Jalal.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 322, no. 3, pp. 731-753. https://doi.org/10.1007/s00220-013-1738-6

}

TY - JOUR

T1 - Scattering for the Zakharov System in 3 Dimensions

AU - Hani, Zaher

AU - Pusateri, Fabio

AU - Shatah, Jalal

PY - 2013/9

Y1 - 2013/9

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.

UR - http://www.scopus.com/inward/record.url?scp=84880506192&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84880506192&partnerID=8YFLogxK

U2 - 10.1007/s00220-013-1738-6

DO - 10.1007/s00220-013-1738-6

M3 - Article

AN - SCOPUS:84880506192

VL - 322

SP - 731

EP - 753

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -