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January/February 2018 Local well-posedness of the NLS equation with third order dispersion in negative Sobolev spaces
Tomoyuki Miyaji, Yoshio Tsutsumi
Differential Integral Equations 31(1/2): 111-132 (January/February 2018).

Abstract

We show the time local well-posedness in $H^s$ of the reduced NLS equation with third order dispersion (r3NLS) on $\mathbf{T}$ for $s > -1/6$. Our proof is based on the nonlinear smoothing effect, which is similar to that for mKdV. However, when (r3NLS) is considered in Sobolev spaces of negative indices, the unconditional uniqueness of solutions, that is, the uniqueness of solutions without auxiliary spaces breaks down in marked contrast to mKdV.

Citation

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Tomoyuki Miyaji. Yoshio Tsutsumi. "Local well-posedness of the NLS equation with third order dispersion in negative Sobolev spaces." Differential Integral Equations 31 (1/2) 111 - 132, January/February 2018.

Information

Published: January/February 2018
First available in Project Euclid: 26 October 2017

zbMATH: 06837089
MathSciNet: MR3717737

Subjects:
Primary: 35A01, 35A02, 35Q53, 35Q55

Rights: Copyright © 2018 Khayyam Publishing, Inc.

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Vol.31 • No. 1/2 • January/February 2018
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