Differential and Integral Equations

Space-time estimates for null gauge forms and nonlinear Schrödinger equations

T. Ozawa and Y. Tsutsumi

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Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equation in one space dimension with interaction satisfying null gauge condition. We prove the local well-posedness of the problem in the Sobolev space $H^{1/2}$. The method depends on the nonlinear gauge transformation and on sharp smoothing estimates for the null gauge form.

Article information

Source
Differential Integral Equations, Volume 11, Number 2 (1998), 201-222.

Dates
First available in Project Euclid: 30 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1367341068

Mathematical Reviews number (MathSciNet)
MR1741843

Zentralblatt MATH identifier
1008.35070

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

Citation

Ozawa, T.; Tsutsumi, Y. Space-time estimates for null gauge forms and nonlinear Schrödinger equations. Differential Integral Equations 11 (1998), no. 2, 201--222. https://projecteuclid.org/euclid.die/1367341068


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