Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
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Abstract:
Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrödinger equation for data in $H^s(\mathbb R)$, $s<1/2$. This result implies that best result concerning local well-posedness for the IVP is in $H^s(\mathbb R), s\ge 1/2$. It is also shown that the (IVP) associated to the generalized Benjamin-Ono equation for data below the scaling is in fact ill-posed.References
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Additional Information
- H. A. Biagioni
- Affiliation: Departamento de Matemática, IMECC-UNICAMP, 13081-970, Campinas, SP, Brasil
- Email: hebe@ime.unicamp.br
- F. Linares
- Affiliation: Instituto de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro, Brasil
- MR Author ID: 343833
- Email: linares@impa.br
- Received by editor(s): April 5, 2000
- Received by editor(s) in revised form: July 24, 2000
- Published electronically: May 3, 2001
- © Copyright 2001 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 353 (2001), 3649-3659
- MSC (1991): Primary 35Q55, 35Q51
- DOI: https://doi.org/10.1090/S0002-9947-01-02754-4
- MathSciNet review: 1837253