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

Biagioni, H.; Linares, F.

doi:10.1090/S0002-9947-01-02754-4

Ill-posedness for the derivative Schrödinger and generalized Benjamin-Ono equations
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by H. A. Biagioni and F. Linares PDF

Trans. Amer. Math. Soc. 353 (2001), 3649-3659 Request permission

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.

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