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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.50 no.1 Bogotá Jan. 2016 


On the well-posedness for the Chen-Lee equation in periodic Sobolev spaces

Sobre el buen planteamiento de la ecuación de Chen-Lee en espacios de Sobolev periódicos

Ricardo Pastrán1, Oscar Riaño1

1 Universidad Nacional de Colombia, Bogotá, Colombia.,


We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation ut + uux + β H uxx + η (H ux - uxx) = 0, where xT, t > 0, η > 0 and H denotes the usual Hilbert transform, is locally and globally well-posed in the Sobolev spaces Hs(T) for any s > -½. We also prove some ill-posedness issues when s < -1.

Keywords: Cauchy problem, local and global well-posedness, Benjamin-Ono equation.

2010 Mathematics Subject Classification: 34A12, 35Q35.


Probamos que el problema de valor inicial asociado a una perturbación de la ecuación de Benjamín-Ono o ecuación de Chen-Lee ut + uux + β H uxx + η (H ux - uxx) = 0, donde xT, t > 0, η > 0 y H denota la transformada de Hilbert usual, es localmente y globalmente bien planteado en espacios de Sobolev Hs(T) para cualquier s > -½. También probamos un tipo de mal planteamiento cuando s < -1.

Palabras claves: Problema de Cauchy, buen planteamiento local y global, ecuación de Benjamín-Ono.

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(Recibido: julio de 2015 Aceptado: enero de 2016)

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