Unconditional uniqueness for the derivative nonlinear Schrödinger equation on the real line

@article{Mosincat2018UnconditionalUF,
  title={Unconditional uniqueness for the derivative nonlinear Schr{\"o}dinger equation on the real line},
  author={Razvan O. Mosincat and Haewon Yoon},
  journal={arXiv: Analysis of PDEs},
  year={2018}
}
We prove the unconditional uniqueness of solutions to the derivative nonlinear Schr\"odinger equation (DNLS) in an almost end-point regularity. To this purpose, we employ the normal form method and we transform (a gauge-equivalent) DNLS into a new equation (the so-called normal form equation) for which nonlinear estimates can be easily established in $H^s(\mathbb{R})$, $s>\frac12$, without appealing to an auxiliary function space. Also, we prove that low-regularity solutions of DNLS satisfy the… 
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  • Nobu Kishimoto
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2022

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