Refinement of Strichartz estimate for Airy equation in non-diagonal case and its application

2017/03/15 by Satoshi Masaki, Masaki, Satoshi, Jun‐ichi Segata +2
Engineering · Mathematics · #35B40 (Secondary) #35Q53 #54C35 (Primary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Mathematical Analysis and Transform Methods #math.AP #msc:35B40 #msc:35Q53 #msc:54C35

paper · pdf · doi:10.48550/arxiv.1703.04892

openalex publication_date 2017/03/15 · arxiv created 2017/04/27 · arxiv updated 2017/04/28 · openalex created_date 2017/04/28 · openalex updated_date 2026/07/28

Abstract

In this paper, we give an improvement of the Strichartz estimate for Airy equation in the non-diagonal case. As an application, we prove the small data scattering and existence of a special non-scattering solutions, which are minimal in suitable sense, to the mass-subcritical generalized Korteweg-de Vries (gKdV) equation. Especially, we remove several technical restrictions on our previous work about the existence of a special non-scattering solution.

Related

• Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation
• Strichartz type estimates of the Airy equation
• About the wave equation outside two strictly convex obstacles
• Scattering problem for the generalized Korteweg-de Vries equation
• Strichartz estimates without loss outside two strictly convex obstacles