Transactions of the American Mathematical Society

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

Author(s): H. A. Biagioni; F. Linares
Journal: Trans. Amer. Math. Soc. 353 (2001), 3649-3659.
MSC (1991): Primary 35Q55, 35Q51
Posted: May 3, 2001
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Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrödinger equation for data in $H^s(\mathbb R)$ ,

. This result implies that best result concerning local well-posedness for the IVP is in $H^s(\mathbb R),\, s\ge1/2$ . It is also shown that the (IVP) associated to the generalized Benjamin-Ono equation for data below the scaling is in fact ill-posed.

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H. A. Biagioni
Affiliation: Departamento de Matemática, IMECC-UNICAMP, 13081-970, Campinas, SP, Brasil
Email: hebe@ime.unicamp.br

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