Unconditional local well-posedness for periodic NLS

Nobu Kishimoto

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arXiv · 1912.12704

Unconditional local well-posedness for periodic NLS

Nobu Kishimoto

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Abstract

The nonlinear Schr\"odinger equations with nonlinearities $|u|^{2k}u$ on the $d$-dimensional torus are considered for arbitrary positive integers $k$ and $d$. The solution of the Cauchy problem is shown to be unique in the class $C_tH^s_x$ for a certain range of scale-subcritical regularities $s$, which is almost optimal in the case $d\geq 4$ or $k\geq 2$. The proof is based on various multilinear estimates and the infinite normal form reduction argument.

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Nobu Kishimoto. 2019-12-29. Unconditional local well-posedness for periodic NLS. https://arxiv.org/abs/1912.12704

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