Preprints and Recent Publications
On the Benjamin and Related Equations
, (with Christian Klein, Didier Pilod, and Jean-Claude Saut).
Well-Posedness for the Extended Schrödinger-Benjamin-Ono System
, (with Argenis Mendez and Didier Pilod). To appear in Vietnam Journal of Mathematics.
On local energy decay for solutions of the Benjamin-Ono equation
, (with Ricardo Freire, Claudio Muñoz, and Gustavo Ponce). To appear in Ann. Inst. H. Poincaré C Anal. Non Linéaire.
Well-posedness for the initial value problem associated to the Zakharov-Kuznetsov (ZK) equation in assymetric spaces
, (with Emile Deléage). Partial Differential Equations and Applications, 4 (2023), no. 2, 9.
On unique continuation for non-local dispersive models
, (with Gustavo Ponce). Vietnam Journal of Mathematics, 51 (2023), no. 4, 771--797.
Propagation of regularity and decay of solutions to nonlinear dispersive equations
, (with Gustavo Ponce). To appear in Matemática Contemporanea
On long time behavior of solutions of the Schrödinger-Korteweg-de Vries system
, (with Argenis J. Mendez). SIAM J. Mathematical Analysis 53 (2021), no. 4, 3838-3855.
Maximal function estimates and local well-posedness for the generalized Zakharov--Kuznetsov equation
, (with Joao P.G. Ramos). SIAM J. Mathematical Analysis 53 (2021), no. 1, 914-936
The Cauchy problem for the L2 critical generalized Zakharov-Kuznetsov equation in dimension 3
, (with Joao P.G. Ramos). Comm. Partial Differential Equations 46 (2021), no. 9, 1601-1627.
Existence of solutions for the surface electromigration equation
, (with Ademir Pastor and Marcia Scialom). Nonlinearity 34 (2021), no. 8, 5213-5233.
Dispersive blow-up for solutions of the Zakharov-Kuznetsov equation
, (with Ademir Pastor and Jorge Drumond Silva). Ann. Inst. H. Poincaré C Anal. Non Linéaire 38 (2021), no. 2, 281-300.
Asymptotic behavior of solutions of the dispersion generalized Benjamin-Ono equation
, (with Argenis Mendez and Gustavo Ponce). Journal of Dynamics and Differential Equations 33 (2021), no. 2, 971-984
Unique continuation properties for solutions to the Camassa-Holm equation and related models
, (with Gustavo Ponce). Proceedings of the American Mathematical Society 148 (9) (2020), 3871-3879.
Properties of solutions to the Camassa-Holm equation on the line in a class containing the peakons
, (with Gustavo Ponce and Thomas Sideris) Advanced Studies in Pure Mathematics 81, 2019. Asymptotic Analysis for Nonlinear Dispersive Equations. 197-246.
On a higher dimensional version of the Benjamin--Ono equation
, (with Oscar G. Riano, Keith M. Rogers, James Wright,and Jonathan Hickman). SIAM Journal of Mathematical Analysis, 51 (2019), 4544-4569.
Dispersive blow-up and persistence properties for the Schrodinger-Korteweg-de Vries equation
, (with Jose M. Palacios). Nonlinearity 32 (2019), 4996-5016.
On a class of solutions to the generalized derivative Schrödinger equations II
, (with Gustavo Ponce and Gleison N. Santos). Journal of Differential Equations 267 (2019), 97-118.
On the periodic Zakharov-Kuznetsov equation
, (with Mahendra Panthee, Tristan Robert,and Nikolay Tzvetkov). Dynamical and Continuous Dynamics Systems 39 (2019), 3521-3533.
Uniqueness results for Zakharov-Kuznetsov equation
, (with Lucrezia Cossetti and Luca Fanelli). Communications Partial Differential Equations 44 (2019), 504-544,
On a class of solutions to the generalized KdV type equation
, (with Hayato Miyazaki and Gustavo Ponce). Commun. Contemp. math. 21 (2019), 1850056, 21 pp.
On a class of solutions to the generalized derivative Schrodinger equations
, (with Gustavo Ponce and Gleison N. Santos). Acta Math. Sin (engl. Ser) 35 (2019), 1057-1073.
Large data scattering for the defocusing supercritical generalized KdV equation
, (with Luiz G. Farah, Ademir Pastor and Nicola Visciglia). Comm. Partial Differential Equations 43 (2018), 118-157.
The Cauchy problem for the fractional Kadomtsev-Petviashvili equations
, (with Didier Pilod and Jean-Claude Saut). SIAM J. Math. Anal. 50 (2018), 118-157.
On Whitham and related equations
, (with Christian Klein, Didier Pilod, and Jean-Claude Saut) Studies in Applied Math. 140 (2018), 133-177.
On Special Regularity Properties of Solutions of the Zakharov-Kusnetsov Equation
, (with Gustavo Ponce) Comm. Pure and Applied Analysis 17 (2018), 1561-1572.
On the regularity of solutions to the k-generalized Korteweg-de Vries equation
, (with Carlos E. Kenig, Gustavo Ponce and Luis Vega) Proceeding of AMS 146 (2018), 3759-3766.
On the regularity of solutions to a class of nonlinear dispersive equations
, (with Gustavo Ponce and Derek L. Smith) Math. Ann. 369 (2017), p. 797-837.