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