| 発表言語 |
日本語
|
| 開催日 |
2010年09月03日 15時30分
|
| 終了日 |
2010年09月03日 17時00分
|
| 開催場所 | 京都大学理学部３号館251号室 |
| セミナー名 | NLPDEセミナー |
| タイトル |
Normal forms and the "upside-down" I method: growth of higher Sobolev norms for periodic NLS. |
| 分野 |
解析
|
| 講演者名 | Tadahiro Oh |
| 講演者所属 | Princeton University |
| 概要 | Bourgain used normal form reduction and the I-method to
prove global well-posedness of one-dimensional periodic quintic NLS in
low regularity. In this talk, we discuss the basic notion of normal
form reduction for Hamiltonian PDEs and apply it to one-dimensional
periodic NLS with general power nonlinearity. Then, we combine it
with the "upside-down" I-method to obtain upperbounds on growth of
higher Sobolev norms of solutions. In the case of cubic NLS, we
explicitly compute the terms arising in the first few iterations of
normal form reduction to improve the result. This is a joint work
with James Colliander (University of Toronto) and Soonsik Kwon
(KAIST). |
|