Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus

Takamori Kato

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arXiv · 2501.11455

Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus

Takamori Kato

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Abstract

We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\mathbb{T}) when s \geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms cannot be defined in the space-time distribution framework for s<1. The main idea is to employ the normal form reduction and a kind of cancellation property to deal with derivative losses.

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Takamori Kato. 2025-01-20. Unconditional well-posendness for the fourth order nonlinear Schrodinger type equations on the torus. https://arxiv.org/abs/2501.11455

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