Ill-posedness for the derivative Schrodinger and generalized Benjamin-Ono equations

Authors
Biagioni, HA Linares, F
Citation
Ha. Biagioni et F. Linares, Ill-posedness for the derivative Schrodinger and generalized Benjamin-Ono equations, T AM MATH S, 353(9), 2001, pp. 3649-3659
Citations number
24
Categorie Soggetti
Mathematics
Journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN journal
00029947 → ACNP
Volume
353
Issue
9
Year of publication
2001
Pages
3649 - 3659
Database
ISI
SICI code
0002-9947(2001)353:9<3649:IFTDSA>2.0.ZU;2-G
Abstract
Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrodinger equation for data in H-s (R), s < 1/2. This result implies that best result concerning local well-posedness f or the IVP is in H-s ( R), s <greater than or equal to> 1/2. It is also sho wn that the (IVP) associated to the generalized Benjamin-Ono equation for d ata below the scaling is in fact ill-posed.