The profile decomposition for the hyperbolic schrÖdinger equation

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

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

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 languageEnglish (US)
Pages (from-to)293-320
Number of pages28
JournalIllinois Journal of Mathematics
Volume62
Issue number1-4
DOIs
StatePublished - 2018

Bibliographical note

Funding Information:
The first author was supported in part by U.S. NSF Grant DMS-1500424. The second author was supported in part by U.S. NSF Grants DMS-1312874 and DMS-1352353. The third author was supported in part by U.S. NSF Grant DMS-1558729 and a Sloane Research fellowship. The fourth author was supported in part by U.S. NSF Grant DMS-1516565. We wish to thank Andrea Nahmod, Klaus Widmayer, Daniel Tataru, Nathan Totz for helpful conversations during the production of this work. Part of this work was initiated when some of the authors were at the Hausdorff Research Institute for Mathematics in Bonn, then progressed during visits to the Institut des Hautes Études in Paris, the Mathematical Sciences Research Institute in Berkeley and the Institute for Mathematics and Applications in Minneapolis. The authors would like to thank these institutions for hosting subsets of them at various times in the last several years.

Funding Information:
Grant DMS-1500424. The second author was supported in part by U.S. NSF Grants DMS-1312874 and DMS-1352353. The third author was supported in part by U.S. NSF Grant DMS-1558729 and a Sloane Research fellowship. The fourth author was supported in part by U.S. NSF Grant DMS-1516565. We wish to thank Andrea Nahmod, Klaus Widmayer, Daniel Tataru, Nathan Totz for helpful conversations during the production of this work. Part of this work was initiated when some of the authors were at the Hausdorff Research Institute for Mathematics in Bonn, then progressed during visits to the Institut des Hautes Études in Paris, the Mathematical Sciences Research Institute in Berkeley and the Institute for Mathematics and Applications in Minneapolis. The authors would like to thank these institutions for hosting subsets of them at various times in the last several years.

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