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arXiv · 2012.09933

Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schr\"odinger Equation

Bradley Isom·Dionyssios Mantzavinos·Atanas Stefanov
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Abstract

A polynomial-in-time growth bound is established for global Sobolev $H^s(\mathbb T)$ solutions to the derivative nonlinear Schr\"odinger equation on the circle with $s>1$. These bounds are derived as a consequence of a nonlinear smoothing effect for an appropriate gauge-transformed version of the periodic Cauchy problem, according to which a solution with its linear part removed possesses higher spatial regularity than the initial datum associated with that solution.

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Bradley Isom, Dionyssios Mantzavinos, Atanas Stefanov. 2020-12-17. Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schr\"odinger Equation. https://arxiv.org/abs/2012.09933

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