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

Felipe Linares | Biagioni, Hebe A.

Keywords: Ill-Posedness | Schrodinger equation | Benjamin-Ono equation

It is established ill-posedness for the initial value problem(IVP) associated to the derivative nonlinear Schrodinger equation for data in Sobolev spaces of order less than 1/2.This result implies that the best result regarding local well-posedness for the IVP is in Sobolev spaces of ordergreater or equal to 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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