## Differential and Integral Equations

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

#### 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

#### 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