2012年
LOCAL WELL-POSEDNESS OF THE KDV EQUATION WITH QUASI-PERIODIC INITIAL DATA
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
- 巻
- 44
- 号
- 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
- ID情報
-
- DOI : 10.1137/110849973
- ISSN : 0036-1410
- eISSN : 1095-7154
- Web of Science ID : WOS:000310576900012