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).
Publisher Copyright:
© 2018 Society for Industrial and Applied Mathematics.
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.
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U2 - 10.1137/17M1153893
DO - 10.1137/17M1153893
M3 - Article
AN - SCOPUS:85049598782
SN - 0036-1410
VL - 50
SP - 2839
EP - 2866
JO - SIAM Journal on Mathematical Analysis
JF - SIAM Journal on Mathematical Analysis
IS - 3
ER -