Research
Research
Partial differential equations, fluid dynamics, harmonic analysis, and their applications. I am mainly interested in studying questions in well-posedness, global behavior, solitary wave solutions, and smoothing properties for solutions of partial differential equations of dispersive type.
Existence and uniqueness of radial solutions of semi-linear equations on manifolds, J. Math. Anal., 554 (1) (2026), joint with Nicolas Martinez-Alba. [Journal] [Arxiv]
On the well-posedness of the periodic fractional Schrödinger equation. PDEA, 6 (31) (2025), joint with Beckett Sanchez and Svetlana Roudenko. [Journal] [Arxiv]
On the Decay of Solutions for the Negative Fractional KdV Equation. J. Fourier Anal. Appl., 31 (2025), joint with Alysson Cunha and Ademir Pastor. [Journal] [Arxiv]
Well-posedness results for a family of dispersive–dissipative Benjamin–Ono equations. Appl. Anal., (2024), 1-33, joint with Ricardo Pastrán. [Journal]
The generalized fractional KdV equation in weighted Sobolev spaces. Comm. Pure Appl. Anal., 21 (2) (2025), joint with Alysson Cunha. [Journal] [Arxiv]
On the persistence properties for the fractionary BBM equation with low dispersion in weighted Sobolev spaces. Nonlinear Analysis, 250, (2025), 113653, joint with Germán Fonseca and Guillermo Rodríguez-Blanco, preprint [Journal] [Arxiv]
On decay properties for solutions of the Zakharov–Kuznetsov equation. Nonlinear Analysis: Real World Applications, 81, (2025), 104183, joint with Argenis Mendez. [Journal] [Arxiv]
Spatial decay properties for a model in shear flows posed on the cylinder. Nonlinear Analysis, 241, (2024), 113473, joint with Ricardo Pastrán [Journal] [Arxiv]
Well-posedness and dynamics of solutions to the generalized KdV with low power nonlinearity. Nonlinearity, 36 (1) (2023), 584–635, joint with Isaac Friedman, Svetlana Roudenko, Diana Son, and Kai Yang [Journal] [Arxiv]
Well-posedness in weighted spaces for the generalized Hartree equation with p<2. Commun. Contemp. Math. 24 (9) (2022), Paper No. 2150074, 51 pp, joint with Anudeep K. Arora and Svetlana Roudenko. [Journal] [Arxiv]
On some regularity properties for the dispersive generalized Benjamin-Ono-Zakharov-Kuznetsov Equation. J. Differential Equations, 322:135–179, (2022), joint with Ricardo C. Freire and Argeniz Mendez. [Journal] [Arxiv]
Higher dimensional generalization of the Benjamin-Ono equation: 2D case. Stud. Appl. Math. (2021), 1–45, joint with Svetlana Roudenko, and Kai Yang. [Journal] [Arxiv]
On persistence properties in weighted spaces for solutions of the fractional Korteweg-de Vries equation. Nonlinearity, 34 (7) (2021), 4604-4660. [Journal] [Arxiv]
Well-posedness for a two-dimensional dispersive model arising from capillary-gravity flows. J. Differential Equations, 280 (2021), 1-65. [Journal] [Arxiv]
The IVP for a Higher dimension version of the Benjamin-Ono equation in weighted Sobolev spaces. Journal Funct. Anal., 279 (8) (2020),108707. [Journal] [Arxiv]
On a higher dimensional version of the Benjamin-Ono equation. SIAM J. Math. Anal., 51 (6) (2019), 4544–4569, joint with Jonathan Hickman, Felipe Linares, Keith Rogers, and James Wright. [Journal] [Arxiv]
Sharp well-posedness for the Chen-Lee equation. Comm. Pure Appl. Anal., 15 (6) (2016), 2179-2202, joint with Ricardo Pastrán. [Journal] [Arxiv].
On the well-posedness for the Chen-Lee equation in periodic Sobolev spaces. Rev. Colombiana Mat., 50 (1) (2016), 55-73, joint with Ricardo Pastrán. [Journal] [Arxiv].
On Kato's smoothing effects for KdV and Benjamin type equations, joint with Carlos Garzón, preprint (Submitted).
Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions, joint with Svetlana Roudenko, preprint (Submitted). [Arxiv].