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

TL;DR

This paper improves the Strichartz estimate for the Airy equation in the non-diagonal case and applies it to establish small data scattering and special non-scattering solutions for the gKdV equation, removing previous technical restrictions.

Contribution

It provides a refined Strichartz estimate for the Airy equation in the non-diagonal case and applies it to prove new results on the existence of special solutions for the gKdV equation.

Findings

Improved Strichartz estimate for Airy in non-diagonal case

Existence of minimal non-scattering solutions for gKdV

Removal of technical restrictions from previous work

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.