# American Institute of Mathematical Sciences

July  2000, 6(3): 625-644. doi: 10.3934/dcds.2000.6.625

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

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

Received  September 1999 Revised  February 2000 Published  April 2000

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.
Citation: Olivier Goubet. Asymptotic smoothing effect for weakly damped forced Korteweg-de Vries equations. Discrete and Continuous Dynamical Systems, 2000, 6 (3) : 625-644. doi: 10.3934/dcds.2000.6.625
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