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Séminaire Laurent Schwartz — EDP et applications

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Herbert Koch
Bounds for KdV and the 1-d cubic NLS equation in rough function spaces
Séminaire Laurent Schwartz — EDP et applications (2011-2012), Exp. No. 11, 10 p., doi: 10.5802/slsedp.8
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Résumé - Abstract

We consider the cubic Nonlinear Schrödinger Equation (NLS) and the Korteweg-de Vries equation in one space dimension. We prove that the solutions of NLS satisfy a-priori local in time $H^{s}$ bounds in terms of the $H^s$ size of the initial data for $s \ge -\frac{1}{4}$ (joint work with D. Tataru, [15, 14]) , and the solutions to KdV satisfy global a priori estimate in $H^{-1}$ (joint work with T. Buckmaster [2]).


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