Abstract
We show the well-posedness in $H^{\frac 12 }$ of the Cauchy problem for a certain class of one dimensional nonlinear Schrödinger equations with the derivative nonlinearity. This is an improvement of results in $H^1$ by N. Hayashi and T. Ozawa [2,3,4,20]. Our results can cover the derivative nonlinear Schrödinger equation. Our proof is based on the Fourier restriction norm method and the gauge transformation.
Citation
Hideo Takaoka. "Well-posedness for the one-dimensional nonlinear Schrödinger equation with the derivative nonlinearity." Adv. Differential Equations 4 (4) 561 - 580, 1999. https://doi.org/10.57262/ade/1366031032
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