Electron. J. Diff. Eqns., Vol. 2008(2008), No. 55, pp. 1-7.

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

Xavier Carvajal

Abstract:
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.

Submitted March 13, 2008. Published April 17, 2008.
Math Subject Classifications: 35A07, 35Q53.
Key Words: Modified KdV equation; KdV equation; local smoothing effect.

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Xavier Carvajal
Instituto de Matemática - UFRJ
Av. Horácio Macedo, Centro de Tecnologia, Cidade Universitária
Ilha do Fundão, Caixa Postal 68530 21941-972 Rio de Janeiro, RJ, Brasil
email: carvajal@im.ufrj.br

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