Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation-Reference-Cited by-同舟云学术

Asymptotic lower bound for the radius of spatial analyticity to solutions of KdV equation

Published:2019-10-20 Issue:08 Volume:21 Page:1850061
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Tesfahun Achenef¹

Affiliation:

1. Department of Mathematics, University of Bergen, P. O. Box 7803, 5020 Bergen, Norway

Abstract

It is shown that the uniform radius of spatial analyticity [Formula: see text] of solutions at time [Formula: see text] to the KdV equation cannot decay faster than [Formula: see text] as [Formula: see text] given initial data that is analytic with fixed radius [Formula: see text]. This improves a recent result of Selberg and da Silva, where they proved a decay rate of [Formula: see text] for arbitrarily small positive [Formula: see text]. The main ingredients in the proof are almost conservation law for the solution to the KdV equation in space of analytic functions and space-time dyadic bilinear [Formula: see text] estimates associated with the KdV equation.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021919971850061X

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