New lower bounds on the radius of spatial analyticity for the KdV equation

2018/04/04 by Huang, Jianhua, Wang, Ming · 1 citation
#35L30 #35Q53 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1804.01628

Abstract

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than t^-1/4 as time t goes to infinity. This improves the works [Selberg, da Silva, Lower bounds on the radius of spatial analyticity for the KdV equation, Annales Henri Poincaré, 2017, 18(3): 1009-1023] and [Tesfahun, Asymptotic lower bound for the radius of spatial analtyicity to solutions of KdV equation, arXiv preprint arXiv:1707.07810, 2017]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.

Cited by

• On the radius of spatial analyticity for the Majda-Biello and Hirota-Satsuma systems

Related

• Asymptotic lower bound for the radius of spatial analtyicity to solutions of KdV equation
• Lower bounds on the radius of spatial analyticity for the KdV equation
• Improved algebraic lower bound for the radius of spatial analyticity for the generalized KdV equation
• Improved lower bound for the radius of analyticity for the modified KdV equation
• Lower bound on the radius of analyticity of solution for fifth order KdV-BBM Equation