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Mathematics > Analysis of PDEs

arXiv:1804.01628 (math)
[Submitted on 4 Apr 2018]

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

Authors:Jianhua Huang, Ming Wang
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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.
Comments: 34pages,0figures
Subjects: Analysis of PDEs (math.AP)
MSC classes: 35Q53, 35L30
Cite as: arXiv:1804.01628 [math.AP]
  (or arXiv:1804.01628v1 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1804.01628

Submission history

From: Ming Wang [view email]
[v1] Wed, 4 Apr 2018 23:53:35 UTC (24 KB)
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