Abstract. Ill-posedness is established for the initial value problem (IVP) associated to the derivative nonlinear Schrödinger equation for data in H s (R), s < 1/2. This result implies that best result concerning local well-posedness
Ž. We establish global well-posedness for the initial value problem IVP associated to the so-called Benney᎐Lin equation. This model is a Korteweg᎐de Vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics. We also study the limiting behaviour of solutions to this IVP when the parameters of the perturbed terms approach 0. ᮊ 1997 Academic Press
Abstract. We establish local and global well-posedness for the modified Zakharov-Kuznetsov equation for initial data in H 1 (R 2 ). We use smoothing estimates for solutions of the linear problem plus a fixed point theorem to prove the local result.
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