論文

査読有り
2012年

LOCAL WELL-POSEDNESS OF THE KDV EQUATION WITH QUASI-PERIODIC INITIAL DATA

SIAM JOURNAL ON MATHEMATICAL ANALYSIS
  • Kotaro Tsugawa

44
5
開始ページ
3412
終了ページ
3428
記述言語
英語
掲載種別
研究論文(学術雑誌)
DOI
10.1137/110849973
出版者・発行元
SIAM PUBLICATIONS

We prove the local well-posedness for the Cauchy problem of the Korteweg-de Vries equation in a quasi-periodic function space. The function space contains functions such that f = f(1) + f(2) + ... + f(N) where f(j) is in the Sobolev space of order s > -1/2N of 2 pi alpha(-1)(j) periodic functions. Note that f is not a periodic function when the ratio of periods alpha(i)/alpha(j) is irrational. The main tool of the proof is the Fourier restriction norm method introduced by Bourgain. We also prove an ill-posedness result in the sense that the flow map (if it exists) is not C-2, which is related to the Diophantine problem.

リンク情報
DOI
https://doi.org/10.1137/110849973
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000310576900012&DestApp=WOS_CPL
ID情報
  • DOI : 10.1137/110849973
  • ISSN : 0036-1410
  • eISSN : 1095-7154
  • Web of Science ID : WOS:000310576900012

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