Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations |
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Authors: | H. A. Biagioni F. Linares |
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Affiliation: | Departamento de Matemática, IMECC-UNICAMP, 13081-970, Campinas, SP, Brasil ; Instituto de Matemática Pura e Aplicada, 22460-320, Rio de Janeiro, Brasil |
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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 , . 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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Keywords: | Ill-posedness, Schr" odinger equation, Benjamin-Ono equation |
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