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

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.

References in corpus (3)

• On well-posedness of generalized Korteweg-de Vries equation in scale critical ^L^r space
• Two minimization problems on non-scattering solutions to mass-subcritical nonlinear Schrödinger equation
• Existence of a minimal non-scattering solution to the mass-subcritical generalized Korteweg-de Vries equation