The Cauchy problem associated to the Benjamin equation in weighted Sobolev spaces

Abstract

We study the initial value problem associated to the Benjamin equation. Our purpose here is to establish persistence properties and some unique continuation properties of the solutions of this equation in weighted Sobolev spaces.

The IVP for a nonlocal perturbation of the Benjamin-Ono equation in classical and weighted Sobolev spaces

“…Fonseca, Linares and Ponce obtained, with the same techniques, similar results for the dispersion generalized Benjamin-Ono equation in [12]. For results regarding well-posenedness in these weighted spaces for other dispersive equations as gKdV, Zakharov-Kuznetsov, Benjamin, and Schrödinger see [13], [3] and [14], [20], [26], respectively. Remark 1.2.…”

The Zakharov–Kuznetsov equation in weighted Sobolev spaces

“…Some relevant nonlinear evolution equations as the KdV equation, the non-linear Schrödinger equation and the Benjamin-Ono equation, have also been studied in the context of weighted Sobolev spaces (see [6], [7], [11], [12], [13], [22], [23] and [24] and references therein).…”

The IVP for the Benjamin–Ono–Zakharov–Kuznetsov equation in low regularity Sobolev spaces

“…On the other hand, to prove Theorem B, the authors employed a truncation-type argument introduced quite recently in [14] to study the IVP associated with the BO equation (1.1) in weighted Sobolev spaces. This technique has been shown to be a powerful tool in order to study the IVP associated with nonlinear dispersive equations in weighted Soboev spaces (see e.g., [4], [5] [15], [16], [17], [18], [21], and references therein).…”