Analysis & PDE

  • Anal. PDE
  • Volume 8, Number 8 (2015), 2029-2055.

Well-posedness and scattering for the Zakharov system in four dimensions

Ioan Bejenaru, Zihua Guo, Sebastian Herr, and Kenji Nakanishi

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Abstract

The Cauchy problem for the Zakharov system in four dimensions is considered. Some new well-posedness results are obtained. For small initial data, global well-posedness and scattering results are proved, including the case of initial data in the energy space. None of these results are restricted to radially symmetric data.

Article information

Source
Anal. PDE, Volume 8, Number 8 (2015), 2029-2055.

Dates
Received: 4 April 2015
Accepted: 3 September 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.apde/1510843187

Digital Object Identifier
doi:10.2140/apde.2015.8.2029

Mathematical Reviews number (MathSciNet)
MR3441212

Zentralblatt MATH identifier
1331.35093

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Keywords
nonlinear wave equation nonlinear Schrödinger equation Zakharov system well-posedness scattering

Citation

Bejenaru, Ioan; Guo, Zihua; Herr, Sebastian; Nakanishi, Kenji. Well-posedness and scattering for the Zakharov system in four dimensions. Anal. PDE 8 (2015), no. 8, 2029--2055. doi:10.2140/apde.2015.8.2029. https://projecteuclid.org/euclid.apde/1510843187


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