The profile decomposition for the hyperbolic schrÖdinger equation

Benjamin Dodson; Jeremy L. Marzuola; Benoit Pausader; Daniel P. Spirn

doi:10.1215/ijm/1552442664

The profile decomposition for the hyperbolic schrÖdinger equation

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

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

In this note, we prove the profile decomposition for hyperbolic Schrödinger (or mixed signature) equations on 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 Ḣ ^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.

Original language	English (US)
Pages (from-to)	293-320
Number of pages	28
Journal	Illinois Journal of Mathematics
Volume	62
Issue number	1-4
DOIs	https://doi.org/10.1215/ijm/1552442664
State	Published - 2018

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© 2019 University of Illinois.

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abstract = " In this note, we prove the profile decomposition for hyperbolic Schr{\"o}dinger (or mixed signature) equations on 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 Ḣ 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.",

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AU - Spirn, Daniel P.

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AB - In this note, we prove the profile decomposition for hyperbolic Schrödinger (or mixed signature) equations on 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 Ḣ 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.

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The profile decomposition for the hyperbolic schrÖdinger equation

Abstract

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