New Lower Bounds of Spatial Analyticity Radius for the Kawahara Equation

Tegegne Getachew

International Journal of Differential Equations, 2025, vol. 2025, 1-8

Abstract: In this paper, an algebraic decay rate for the radius of spatial analyticity of solutions to the Kawahara equation ∂tu+β∂x5u+α∂x3u+u∂xu=0,β≠0 is investigated. With given analytic initial data having a fixed radius of analyticity σ0, we derive an algebraic decay rate σt∼t−1/2 for the uniform radius of spatial analyticity of solutions to the Kawahara equation. This improves a recent result due to Ahn et al.’s study, where they demonstrated a decay rate of order t−1. Our strategy mainly relies on an approximate conservation law in a modified Gevrey space and bilinear estimate in Bourgain space.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijde:2947966

DOI: 10.1155/ijde/2947966

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