Differential and Integral Equations

Well-posedness for the Zakharov system with the periodic boundary condition

Hideo Takaoka

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Abstract

Under a non resonance condition, we establish the unique local existence results in weak function spaces for the initial value problem of the Zakharov system with the periodic boundary condition. The proof is based on the Fourier restriction norm method, which was developed by J. Bourgain and C.E. Kenig, G. Ponce and L. Vega.

Article information

Source
Differential Integral Equations, Volume 12, Number 6 (1999), 789-810.

Dates
First available in Project Euclid: 29 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367241476

Mathematical Reviews number (MathSciNet)
MR1728031

Zentralblatt MATH identifier
1022.35069

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Takaoka, Hideo. Well-posedness for the Zakharov system with the periodic boundary condition. Differential Integral Equations 12 (1999), no. 6, 789--810. https://projecteuclid.org/euclid.die/1367241476


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