Illinois Journal of Mathematics

The profile decomposition for the hyperbolic Schrödinger equation

Benjamin Dodson, Jeremy L. Marzuola, Benoit Pausader, and Daniel P. Spirn

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Abstract

In this note, we prove the profile decomposition for hyperbolic Schrödinger (or mixed signature) equations on $\mathbb{R}^{2}$ in two cases, one mass-supercritical and one mass-critical. First, as a warm up, we show that the profile decomposition works for the ${\dot{H}}^{\frac{1}{2}}$ critical problem. Then, we give the derivation of the profile decomposition in the mass-critical case based on an estimate of Rogers-Vargas (J. Functional Anal. 241(2) (2006), 212–231).

Article information

Source
Illinois J. Math., Volume 62, Number 1-4 (2018), 293-320.

Dates
Received: 13 November 2018
Revised: 13 November 2018
First available in Project Euclid: 13 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1552442664

Digital Object Identifier
doi:10.1215/ijm/1552442664

Mathematical Reviews number (MathSciNet)
MR3922418

Zentralblatt MATH identifier
07036788

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q35: PDEs in connection with fluid mechanics

Citation

Dodson, Benjamin; Marzuola, Jeremy L.; Pausader, Benoit; Spirn, Daniel P. The profile decomposition for the hyperbolic Schrödinger equation. Illinois J. Math. 62 (2018), no. 1-4, 293--320. doi:10.1215/ijm/1552442664. https://projecteuclid.org/euclid.ijm/1552442664


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