| Language |
English
|
| From |
2011/12/27 15:30
|
| To |
2011/12/27 17:00
|
| Place | Room 552, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | NLPDE Seminar |
| Title |
Invariant weighted Wiener measure for the derivative NLS |
| Field |
Analysis
|
| Speakers | Tadahiro Oh |
| Affiliation | Princeton University |
| Abstract | In this talk, we consider the derivative NLS (DNLS) on T.
In particular, we construct a weighted Wiener measure, globally
defined flow almost surely with respect to this measure, and finally
invariance of the measure. The basic idea is to follow Bourgain's
argument ('94.) Due to the nature of nonlinearity and known local
well-/ill-posedness results, we consider DNLS under the gauge
transformation, which causes additional difficulty. In particular,
the finite dimensional measures corresponding to the finite
dimensional approximations are no longer invariant. In the end, we
prove "almost" invariance of such finite dimensional measures via
multilinear estimates to achieve our goal. This is a joint work with
A. Nahmod (UMASS), L. Rey-Bellet (UMASS), and G. Sttafilani (MIT). |
| Link | http://www.math.kyoto-u.ac.jp/~yosihiro/nlpde/nlpde.html |
|