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.
Publications
Spatial decay properties for a model in shear flows posed on the cylinder, Nonlinear Analysis, 241, (2024), 113473, joint with Ricardo Pastán [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 (2022), no. 9, 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].
Preprints
On decay properties for solutions of the Zakharov-Kuznetsov equation, joint with Argeniz Mendez, preprint (Submitted). [Arxiv]
The generalized fractional KdV equation in weighted Sobolev spaces, joint with A. Cunha, preprint (Submitted). [Arxiv]
Stability and instability of solitary waves in fractional generalized KdV equation in all dimensions, joint with Svetlana Roudenko, preprint (Submitted). [Arxiv].