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May/June 2019 Regularity and uniqueness for the rough solutions of the derivative nonlinear Schrödinger equation
Yuanyuan Dan, Yongsheng Li, Cui Ning
Differential Integral Equations 32(5/6): 265-290 (May/June 2019).

Abstract

In this paper, we obtain the unconditional uniqueness for the rough solutions of the derivative nonlinear Schrödinger equation $$ i\partial_t u + \partial^2_{x} u =i\partial_{x}(|u|^2u) $$ in $C([0,T];H^s(\mathbb R))$, $s\in(\frac{2}{3},1]$. The arguments used here are the normal form argument, resonant decomposition and the Bourgain argument. The main ingredient in the proof is to improve the regularity of the solution by iteration method and finally show that the solution belongs to some Bourgain space.

Citation

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Yuanyuan Dan. Yongsheng Li. Cui Ning. "Regularity and uniqueness for the rough solutions of the derivative nonlinear Schrödinger equation." Differential Integral Equations 32 (5/6) 265 - 290, May/June 2019.

Information

Published: May/June 2019
First available in Project Euclid: 3 April 2019

zbMATH: 07088831
MathSciNet: MR3938340

Subjects:
Primary: 35A01, 35Q55

Rights: Copyright © 2019 Khayyam Publishing, Inc.

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Vol.32 • No. 5/6 • May/June 2019
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