Large-data equicontinuity for the derivative NLS

2021/06/24 by Harrop-Griffiths, Benjamin, Killip, Rowan, Visan, Monica · 2 citations
#35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.13333

Abstract

We consider the derivative NLS equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of L² bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.

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• Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
• Global solution and asymptotic behavior for the kinetic derivative NLS on \mathbb R

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