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arXiv · 2409.11002

Global Well-posedness for the Fourth-order Nonlinear Schrodinger Equation

Mingjuan Chen·Yufeng Lu·Yaqing Wang
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Abstract

The local and global well-posedness for the one dimensional fourth-order nonlinear Schr\"odinger equation are established in the modulation space $M^{s}_{2,q}$ for $s\geq \frac12$ and $2\leq q <\infty$. The local result is based on the $U^p-V^p$ spaces and crucial bilinear estimates. The key ingredient to obtain the global well-posedness is that we achieve a-priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip-Visan-Zhang for completely integrable PDEs.

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Mingjuan Chen, Yufeng Lu, Yaqing Wang. 2024-09-17. Global Well-posedness for the Fourth-order Nonlinear Schrodinger Equation. https://arxiv.org/abs/2409.11002

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