Asymptotic stability of solitons for the Benjamin-Ono equation

C. E. Kenig (1) , Yvan Martel (2)

1 Department of Mathematics [Chicago]
2 LMV - Laboratoire de Mathématiques de Versailles

In this paper, we prove the asymptotic stability of the family of solitons of the Benjamin-Ono equation in the energy space. The proof is based on a Liouville property for solutions close to the solitons for this equation, in the spirit of Martel and Merle (arXiv:0706.1174v2). As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.

Domaines: Equations aux dérivées partielles [math.AP]

C. E. Kenig, Yvan Martel. Asymptotic stability of solitons for the Benjamin-Ono equation. Revista Matemática Iberoamericana, 2009, 25 (3), pp.909-970. ⟨10.4171/RMI/586⟩. ⟨hal-00408107⟩