This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with field, including transition to steady state spectra, statistical moments, and distribution functions amplitudes. Numerical simulations are conducted across diff...

We show that the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation ut −D α xux + uxyy = uux, (t, x, y) ∈ R , 1 ≤ α ≤ 2, is locally well-posed in the spaces Es, s > 2 α − 3 4 , endowed with the norm ‖f‖Es = ‖〈|ξ| α + μ〉f̂‖L2(R2). As a consequence, we get the global wellposedness in the energy space E1/2 as soon as α > 8 5 . The proof is based ...

Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is associated with part equation. Altogether, this analysis complemented by unique continuation principles that determine optimal spatial decay. This work intended to estab...

We prove that the Benjamin-Ono equation is globally well-posed in Hs(T) for s ≥ 0. Moreover we show that the associated flow-map is Lipschitz on every bounded set of Hs 0 (T), s ≥ 0, and even real-analytic in this space for small times. This result is sharp in the sense that the flow-map (if it can be defined and coincides with the standard flow-map on H∞ 0 (T)) cannot be of class C , α > 0, fr...