Abstract

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.  https://doi.org/10.15446/recolma.v50n1.62187.

Abstract We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation u_t + uu_x + β H u_xx + η (H u_x - u_xx) = 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 H^s(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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