Oscar G. Riaño

activity

20152026

most citedOn persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation

9 citations · 24 across the 18 of their papers we have counts for

collaborators

22 papers

math.AP2026

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Iryna Petrenko, Oscar Riaño, Svetlana Roudenko

In this paper we consider the 4th order (or biharmonic) nonlinear Schrödinger (NLS) equation in dimensions 1, 2, and 3, where the potential term is expressed as a power non-lineari…

math.AP2026

Decay and regularity properties for the dispersion generalized Benjamin-Ono equation

Germán Fonseca, Oscar Riaño, Guillermo Rodríguez-Blanco

We study spatial decay properties of solutions to the dispersion generalized Benjamin-Ono equation. We first establish persistence properties in weighted Sobolev spaces under a sha…

math.AP2026

On Kato's smoothing effects for KdV and Benjamin type equations

Carlos Garzón, Oscar Riaño

We analyze how the interaction between local and nonlocal dispersions, combined with different types of nonlinearities, influences the smoothing effects of solutions. To achieve th…

math.AP2026

The nonlinear Schrödinger equation with combined nonlinearities in 1D

Oscar Riaño, Alex D Rodriguez, Svetlana Roudenko

We consider the one-dimensional nonlinear Schrödinger equation $i u_{t} + u_{xx} + N (u) u = 0, x, t \in R,$ with the nonlinearity term that is expressed as a s…

math.AP2025

A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation

Argenis J. Méndez, Oscar Riaño

By employing a new class of pseudo-differential operators introduced in a previous work, we establish a novel monotonicity formula for the fractional Laplacian $∣ \nabla_{x} ∣^{α}$ in $\…

math.AP2025

Existence and uniqueness of radial solutions of semi-linear equations on manifolds

Nicolas Martinez-Alba, Oscar Riaño

We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$ . By combining differential…

math.AP2025

On the decay of solutions for the negative fractional KdV equation

Alysson Cunha, Oscar Riaño, Ademir Pastor

We explore the limits of fractional dispersive effects and their incidence in the propagation of polynomial weights. More precisely, we consider the fractional KdV equation when a…

math.AP2024

On the well-posedness of the periodic fractional Schrödinger equation

Beckett Sanchez, Oscar Riaño, Svetlana Roudenko

We consider the periodic fractional nonlinear Schrödinger equation $i u_{t} - (- Δ)^{\frac{s}{2}} u + N (∣ u ∣) u = 0, x \in T^{N}, t \in R, s > 0,$ …

math.AP2024

On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces

Germán Fonseca, Oscar Riaño, Guillermo Rodriguez-Blanco

We consider the initial value problem associated to the low dispersion fractionary Benjamin-Bona-Mahony equation, fBBM. Our aim is to establish local persistence results in weighte…

math.AP2023

Spatial decay properties for a model in shear flows posed on the cylinder

Ricardo A. Pastrán, Oscar Riaño

We study spatial decay properties for solutions of the Pelinovski-Stepanyants equation posed on the cylinder. We establish the maximum polynomial decay admissible for solutions of…

math.AP2023

On decay properties for solutions of the Zakharov-Kuznetsov equation

Argenis J. Mendez, Oscar Riaño

This work mainly focuses on the spatial decay properties of solutions to the Zakharov-Kuznetsov equation. In earlier studies for the two- and three-dimensional cases, it was establ…

math.AP2022★ 2 cited

The generalized fractional KdV equation in weighted Sobolev spaces

Alysson Cunha, Oscar Riaño

This work concerns the study of persistence property in polynomial weighted spaces for solutions of the generalized fractional KdV equation in any spatial dimension $d \geq 1$ . By e…

math.AP2022★ 3 cited

Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions

Oscar Riaño, Svetlana Roudenko

We study stability of solitary wave solutions for the fractional generalized Korteweg-de Vries equation $$ \partial_t u- \partial_{x_1} D^αu+ \tfrac{1}{m}\partial_{x_1}(u^m)=0, ~ (…

math.AP2022★ 8 cited

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Isaac Friedman, Oscar Riaño, Svetlana Roudenko +2

We consider two types of the generalized Korteweg - de Vries equation, where the nonlinearity is given with or without absolute values, and, in particular, including the low powers…

math.AP2021

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Oscar Riaño, Svetlana Roudenko, Kai Yang

We consider a higher-dimensional version of the Benjamin-Ono (HBO) equation in the 2D setting: $u_{t} - R_{1} Δ u + \frac{1}{2} (u^{2})_{x} = 0, (x, y) \in R^{2}$ , which is $L^2…

math.AP2020

Well-posedness in weighted spaces for the generalized Hartree equation with $p < 2$

Anudeep K. Arora, Oscar Riaño, Svetlana Roudenko

We investigate the well-posedness in the generalized Hartree equation $i u_{t} + Δ u + (∣ x ∣^{- (N - γ)} * ∣ u ∣^{p}) ∣ u ∣^{p - 2} u = 0$ , $x \in R^{N}$ , $0 < γ < N$ , for low powers of nonlinea…

math.AP2020★ 9 cited

On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation

Oscar Riaño

Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights…

math.AP2020

On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov Equation

Ricardo. C. Freire, Argenis J. Mendez, Oscar Riaño

This work aims to study some smoothness properties concerning the initial value problem associated to the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov equation. More prec…

math.AP2020

Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows

Oscar Riaño

This paper is aimed to establish well-posedness in several settings for the Cauchy problem associated to a model arising in the study of capillary-gravity flows. More precisely, we…

math.AP2019

The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces

Oscar G. Riaño

We study the initial value problem associated to a higher dimensional version of the Benjamin-Ono equation. Our purpose is to establish local well-posedness results in weighted Sob…

math.AP2019★ 2 cited

On a higher dimensional version of the Benjamin--Ono equation

Felipe Linares, Oscar G. Riaño, Keith M. Rogers +2

We consider a higher dimensional version of the Benjamin--Ono equation, $\partial_{t} u - R_{1} Δ u + u \partial_{x_{1}} u = 0$ , where $R_{1}$ denotes the Riesz transform with…

math.AP2015

On the Well-posedness for the Chen-Lee equation in periodic Sobolev spaces

Ricardo A. Pastrán, Oscar G. Riaño

We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation $u_{t} + u u_{x} + β H u_{xx} + η (H u_{x} - u_{xx}) = 0$ , w…

Local well-posedness for the biharmonic nonlinear Schrödinger equation in low dimensions

Decay and regularity properties for the dispersion generalized Benjamin-Ono equation

On Kato's smoothing effects for KdV and Benjamin type equations

The nonlinear Schrödinger equation with combined nonlinearities in 1D

A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation

Existence and uniqueness of radial solutions of semi-linear equations on manifolds

On the decay of solutions for the negative fractional KdV equation

On the well-posedness of the periodic fractional Schrödinger equation

On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces

Spatial decay properties for a model in shear flows posed on the cylinder

On decay properties for solutions of the Zakharov-Kuznetsov equation

The generalized fractional KdV equation in weighted Sobolev spaces

Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions

Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity

Higher dimensional generalization of the Benjamin-Ono equation: 2D case

Well-posedness in weighted spaces for the generalized Hartree equation with p<2

On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation

On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov Equation

Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows

The IVP for a higher dimensional version of the Benjamin-Ono equation in weighted Sobolev spaces

On a higher dimensional version of the Benjamin--Ono equation

On the Well-posedness for the Chen-Lee equation in periodic Sobolev spaces

Well-posedness in weighted spaces for the generalized Hartree equation with $p < 2$