Differential and Integral Equations

The Cauchy problem for a Schrödinger-Korteweg-de Vries system with rough data

Hartmut Pecher

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Abstract

The Cauchy problem for a coupled system of the Schrödinger and the KdV equation is shown to be globally well posed for data with infinite energy. The proof uses refined bilinear Strichartz-type estimates and the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao.

Article information

Source
Differential Integral Equations, Volume 18, Number 10 (2005), 1147-1174.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060109

Mathematical Reviews number (MathSciNet)
MR2162627

Zentralblatt MATH identifier
1212.35427

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]
Secondary: 35B45: A priori estimates

Citation

Pecher, Hartmut. The Cauchy problem for a Schrödinger-Korteweg-de Vries system with rough data. Differential Integral Equations 18 (2005), no. 10, 1147--1174. https://projecteuclid.org/euclid.die/1356060109


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