Dispersive Decay Bound of Small Data Solutions to Kawahara Equation in a Finite Time Scale

2022/10/06 by Jongwon Lee, Lee, Jongwon
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2210.02712

openalex publication_date 2022/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we prove that small localized data yield solutions to Kawahara type equation which have linear dispersive decay on a finite time. We use the similar method used to derive the dispersive decay bound of the solutions to the KdV equation, with some steps being simpler. This result is expected to be the first result of the small data global bounds of the fifth-order dispersive equations with quadratic nonlinearity.

Related

• Dispersive decay of small data solutions for the KdV equation
• Dispersive decay bound of small data solutions to higher order scattering-supercritical KdV-type equations
• Dispersive limit from the Kawahara to the KdV equation
• Decay properties for solutions of fifth order nonlinear dispersive equations
• Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation