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Enhanced existence time of solutions to the fractional Korteweg de Vries equation

Ehrnstrom, Mats; Wang, Yuexun
Peer reviewed, Journal article
Accepted version
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URI
https://hdl.handle.net/11250/2685513
Date
2019
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  • Institutt for matematiske fag [2672]
  • Publikasjoner fra CRIStin - NTNU [41869]
Original version
SIAM Journal on Mathematical Analysis. 2019, 51 (4), 3298-3323.   10.1137/19M1237867
Abstract
We consider the fractional Korteweg–de Vries equation ut+ uux−|D| αux = 0 in the range of −1 < α < 1, α 6= 0. Using basic Fourier techniques in combination with the modified energy method we extend the existence time of classical solutions with initial data of size ε from 1 ε to a time scale of 1 ε2 . This analysis, which is carried out in Sobolev space HN (R), N ≥ 3, answers positively a question posed by Linares, Pilod and Saut in [SIAM J. Math. Anal., 46 (2014), pp. 1505--1537].
Publisher
Society for Industrial and Applied Mathematics
Journal
SIAM Journal on Mathematical Analysis

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