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1998 Space-time estimates for null gauge forms and nonlinear Schrödinger equations
T. Ozawa, Y. Tsutsumi
Differential Integral Equations 11(2): 201-222 (1998). DOI: 10.57262/die/1367341068


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.


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T. Ozawa. Y. Tsutsumi. "Space-time estimates for null gauge forms and nonlinear Schrödinger equations." Differential Integral Equations 11 (2) 201 - 222, 1998.


Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1008.35070
MathSciNet: MR1741843
Digital Object Identifier: 10.57262/die/1367341068

Primary: 35Q55

Rights: Copyright © 1998 Khayyam Publishing, Inc.

Vol.11 • No. 2 • 1998
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