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 |
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Pages (from-to) | 2839-2866 |
Number of pages | 28 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 50 |
Issue number | 3 |
DOIs | |
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