Refinement of strichartz estimates for airy equation in nondiagonal case and its application

Satoshi Masaki; Jun Ichi Segata

doi:10.1137/17M1153893

Refinement of strichartz estimates for airy equation in nondiagonal case and its application

Satoshi Masaki, Jun Ichi Segata

SCI - Mathematics

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

1 Citation (Scopus)

Abstract

In this paper, we give an improvement of nondiagonal Strichartz estimates for the Airy equation by using a Morrey-type space. As its applications, we prove the small data scattering and the existence of special nonscattering solutions, which are minimal in a suitable sense, to the mass-subcritical generalized Korteweg–de Vries equation. Especially, the use of a refined nondiagonal estimate removes several technical restrictions on the previous work [S. Masaki and J. Segata, Existence of a Minimal Non-Scattering Solution to the Mass-Subcritical Generalized Korteweg-de Vries Equation, preprint, arXiv:1602.05331] about the existence of the special non-scattering solution.

Original language	English
Pages (from-to)	2839-2866
Number of pages	28
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	3
DOIs	https://doi.org/10.1137/17M1153893
Publication status	Published - 2018

Keywords

Airy equation
Generalized Korteweg–de Vries equation
Scattering problem
Strichartz estimate
Threshold solution

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

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10.1137/17M1153893

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title = "Refinement of strichartz estimates for airy equation in nondiagonal case and its application",

abstract = "In this paper, we give an improvement of nondiagonal Strichartz estimates for the Airy equation by using a Morrey-type space. As its applications, we prove the small data scattering and the existence of special nonscattering solutions, which are minimal in a suitable sense, to the mass-subcritical generalized Korteweg–de Vries equation. Especially, the use of a refined nondiagonal estimate removes several technical restrictions on the previous work [S. Masaki and J. Segata, Existence of a Minimal Non-Scattering Solution to the Mass-Subcritical Generalized Korteweg-de Vries Equation, preprint, arXiv:1602.05331] about the existence of the special non-scattering solution.",

keywords = "Airy equation, Generalized Korteweg–de Vries equation, Scattering problem, Strichartz estimate, Threshold solution",

author = "Satoshi Masaki and Segata, {Jun Ichi}",

note = "Funding Information: ∗Received by the editors October 25, 2017; accepted for publication (in revised form) April 6, 2018; published electronically June 5, 2018. http://www.siam.org/journals/sima/50-3/M115389.html Funding: The work of the first author was partially supported by the Sumitomo Foundation, Basic Science Research Projects 161145. The work of the second author was partially supported by JSPS, Grant-in-Aid for Young Scientists (A) 25707004. †Department Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka Osaka, 560-8531, Japan (masaki@sigmath.es.osaka-u.ac.jp). ‡Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai 980–8578, Japan (segata@m.tohoku.ac.jp).",

year = "2018",

doi = "10.1137/17M1153893",

language = "English",

volume = "50",

pages = "2839--2866",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Refinement of strichartz estimates for airy equation in nondiagonal case and its application

AU - Masaki, Satoshi

AU - Segata, Jun Ichi

N1 - Funding Information: ∗Received by the editors October 25, 2017; accepted for publication (in revised form) April 6, 2018; published electronically June 5, 2018. http://www.siam.org/journals/sima/50-3/M115389.html Funding: The work of the first author was partially supported by the Sumitomo Foundation, Basic Science Research Projects 161145. The work of the second author was partially supported by JSPS, Grant-in-Aid for Young Scientists (A) 25707004. †Department Systems Innovation, Graduate School of Engineering Science, Osaka University, Toyonaka Osaka, 560-8531, Japan (masaki@sigmath.es.osaka-u.ac.jp). ‡Mathematical Institute, Tohoku University, 6-3, Aoba, Aramaki, Aoba-ku, Sendai 980–8578, Japan (segata@m.tohoku.ac.jp).

PY - 2018

Y1 - 2018

N2 - In this paper, we give an improvement of nondiagonal Strichartz estimates for the Airy equation by using a Morrey-type space. As its applications, we prove the small data scattering and the existence of special nonscattering solutions, which are minimal in a suitable sense, to the mass-subcritical generalized Korteweg–de Vries equation. Especially, the use of a refined nondiagonal estimate removes several technical restrictions on the previous work [S. Masaki and J. Segata, Existence of a Minimal Non-Scattering Solution to the Mass-Subcritical Generalized Korteweg-de Vries Equation, preprint, arXiv:1602.05331] about the existence of the special non-scattering solution.

AB - In this paper, we give an improvement of nondiagonal Strichartz estimates for the Airy equation by using a Morrey-type space. As its applications, we prove the small data scattering and the existence of special nonscattering solutions, which are minimal in a suitable sense, to the mass-subcritical generalized Korteweg–de Vries equation. Especially, the use of a refined nondiagonal estimate removes several technical restrictions on the previous work [S. Masaki and J. Segata, Existence of a Minimal Non-Scattering Solution to the Mass-Subcritical Generalized Korteweg-de Vries Equation, preprint, arXiv:1602.05331] about the existence of the special non-scattering solution.

KW - Airy equation

KW - Generalized Korteweg–de Vries equation

KW - Scattering problem

KW - Strichartz estimate

KW - Threshold solution

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Refinement of strichartz estimates for airy equation in nondiagonal case and its application

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