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

2024/09/17 by Chen, Mingjuan, Lu, Yufeng, Wang, Yaqing
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.11002

Abstract

The local and global well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation are established in the modulation space M^s_2,q for s≥ \frac12 and 2≤ q <∞. 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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