Asymptotic stability of solitons for the Benjamin-Ono equation
Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, p. 909-970 / Harvested from Project Euclid
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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, Y. and Merle, F.: Asymptotic stability of solitons for subcritical generalized KdV equations. Arch. Ration. Mech. Anal. 157 (2001), 219-254], [Martel, Y. and Merle, F.: Asymptotic stability of solitons of the gKdV equations with a general nonlinearity. Math. Ann. 341 (2008), 391-427]. As a corollary of the proofs, we obtain the asymptotic stability of exact multi-solitons.
Publié le : 2009-06-15
Classification:  Benjamin-Ono equation,  soliton,  asymptotic stability,  Liouville theorem,  35Q53,  35Q51,  35B40 
@article{1257258098,
     author = {Kenig
, 
Carlos E. and Martel
, 
Yvan},
     title = {Asymptotic stability of solitons for the Benjamin-Ono equation},
     journal = {Rev. Mat. Iberoamericana},
     volume = {25},
     number = {1},
     year = {2009},
     pages = { 909-970},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1257258098}
}

Kenig
, 
Carlos E.; Martel
, 
Yvan. Asymptotic stability of solitons for the Benjamin-Ono equation. Rev. Mat. Iberoamericana, Tome 25 (2009) no. 1, pp.  909-970. http://gdmltest.u-ga.fr/item/1257258098/