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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426


PASTRAN, Ricardo  and  RIANO, Oscar. On the well-posedness for the Chen-Lee equation in periodic Sobolev spaces. Rev.colomb.mat. [online]. 2016, vol.50, n.1, pp.55-73. ISSN 0034-7426.

Abstract 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 x ∈ T, 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.

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