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.
Solitary waves in the fractional generalized KdV equation: Stability and instability in $\mathbb{R}^d$. Nonlinear Analysis: Real World Applications, 92, (2026), 104641, joint with Svetlana Roudenko. [Journal] [Arxiv]
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].
The nonlinear Schrôdinger equation with combined nonlinearities in 1D, joint with Alex D. Rodriguez, Svetlana Roudenko, preprint (Submitted) [Arxiv]
A monotonicity formula for the fractional Laplacian and instability results for the Shrira equation, joint with Argenis Mendez, preprint (Submitted) [Arxiv]
On Kato's smoothing effects for KdV and Benjamin type equations, joint with Carlos Garzón, preprint (Submitted).