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

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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