Electronic Journal of Differential Equations (Apr 2008)

A note on local smoothing effects for the unitary group associated with the KdV equation

  • Xavier Carvajal

Journal volume & issue
Vol. 2008, no. 55
pp. 1 – 7

Abstract

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In this note we show interesting local smoothing effects for the unitary group associated to Korteweg-de Vries type equation. Our main tools are the Hardy-Littlewood-Sobolev and Hausdorff-Young inequalities. Using our local smoothing effect and a dual version, we estimate the growth of the norm of solutions of the complex modified KdV equation.

Keywords