Skip to main content
SpringerLink
Log in

On a Degenerate Zakharov System

  • Original Paper
  • Published:
Bulletin of the Brazilian Mathematical Society Aims and scope Submit manuscript

Abstract.

We establish a local well-posedness result for an initial value problem associated to a Zakharov system arising in the study of laser-plasma interactions. We called this system degenerate due to the lack of dispersion presented in one of the spatial variables. One of the key tools to obtain our results is the presence of appropriate global versions of the so called “local smoothing effects” inherent to the dispersive character of the model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, BRAZIL

    F. Linares*

  2. Department of Mathematics, University of California, Santa Barbara, CA 93106, USA

    G. Ponce**

  3. Département de Mathématiques, Université de Paris XI (Paris-Sud), 91405, Orsay, FRANCE

    J-C. Saut

Authors
  1. F. Linares*
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Ponce**
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J-C. Saut
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Linares*.

Additional information

*Partially supported by CNPq-Brazil.

**Partially supported by NSF grant DMS-0140023.

About this article

Cite this article

Linares*, F., Ponce**, G. & Saut, JC. On a Degenerate Zakharov System. Bull Braz Math Soc, New Series 36, 1–23 (2005). https://doi.org/10.1007/s00574-005-0025-3

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00574-005-0025-3

Keywords:

Mathematical subject classification:

Search

Navigation