Bounds for KdV and the 1-d cubic NLS equation in rough function spaces

Herbert Koch

Type: Article

Publication Date: 2014-11-20

Citations: 0

DOI: https://doi.org/10.5802/slsedp.8

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≥-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]).

Locations

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+	Semiclassical soliton ensembles for the focusing nonlinear Schrödinger equation	2003	Spyridon Kamvissis K. T-R McLaughlin Peter D. Miller
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+	On the ill-posedness of some canonical dispersive equations	2001	Carlos E. Kenig Gustavo Ponce Luis Vega
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+ PDF Chat	A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation	1993	Percy Deift Xin Zhou
+	The Korteweg-de-Vries equation at H^{-1} regularity	2011	Tristan Buckmaster Herbert Koch
+	Asymptotic Stability of Solitons¶for Subcritical Generalized KdV Equations	2001	Yvan Martel Frank Merle