Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations

Olivier Goubet

doi:10.3934/dcds.2000.6.625

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2000, Volume 6, Issue 3: 625-644. Doi: 10.3934/dcds.2000.6.625

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Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations

Olivier Goubet^1,

1.
Université de Cergy-Pontoise, Département de Mathématiques, 2 Avenue Adolphe Chauvin, 95302 Cergy-Pontoise

Received: August 31, 1999

Revised: January 31, 2000

Published: June 2000

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Abstract

Weakly damped forced KdV equation provides a dissipative semigroup on $L_x^2$. We prove that this semigroup enjoys an asymptotic smoothing effect, i.e. that all solutions converge towards a set of smoother solutions, when time goes to infinity.

Keywords:

Asymptotic smoothing effect,
weakly damped Korteweg-de Vries equation,
Bourgain spaces,
regularity of the attractor.

Mathematics Subject Classification: 35Q53, 58F12.

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Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations

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