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

Tohru Ozawa, Yoshio Tsutsumi

Type: Article

Publication Date: 1998-01-01

Citations: 48

DOI: https://doi.org/10.57262/die/1367341068

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.

Locations

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