The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces
نویسندگان
چکیده
منابع مشابه
The Ivp for the Dispersion Generalized Benjamin-ono Equation in Weighted Sobolev Spaces
We study the initial value problem associated to the dispersion generalized Benjamin-Ono equation. Our aim is to establish well posedness results in weighted Sobolev spaces and to deduce from them some sharp unique continuation properties of solutions to this equation. In particular, we shall establish optimal decay rate for the solutions of this model. RÉSUMÉ. Nous étudions le problème de Cauc...
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We develop a perturbation theory for the Benjamin–Ono (BO) equation. This perturbation theory is based on the inverse scattering transform for the BO equation, which was originally developed by Fokas and Ablowitz and recently refined by Kaup and Matsuno. We find the expressions for the variations of the scattering data with respect to the potential, as well as the dual expression for the variat...
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Here we continue the study of the initial value problem for the third order Benjamin-Ono equation in the weighted Sobolev spaces Hs γ = H s⋂L2γ , where s > 3, γ ≥ 0. The result is the proof of well-posedness of the afore mentioned problem in Hs γ , s > 3, γ ∈ [0, 1]. The proof involves the use of parabolic regularization, the Riesz-Thorin interpolation theorem and the construction technique of ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2019
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2019.03.047