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

Authors:
H. A. Biagioni and F. Linares

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

Published electronically:
May 3, 2001

MathSciNet review:
1837253

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrödinger equation for data in , . This result implies that best result concerning local well-posedness for the IVP is in . 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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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

Email:
linares@impa.br

DOI:
https://doi.org/10.1090/S0002-9947-01-02754-4

Keywords:
Ill-posedness,
Schr\"odinger equation,
Benjamin-Ono equation

Received by editor(s):
April 5, 2000

Received by editor(s) in revised form:
July 24, 2000

Published electronically:
May 3, 2001

Article copyright:
© Copyright 2001
American Mathematical Society