My research focuses in nonlinear dispersive equations. In particular my main works are related to the study of existence and properties of solutions to one dimensional models. Some of my areas of expertise are:

• The study of Cauchy problems posed in Sobolev spaces.

• The study persistence of solutions in weighted Sobolev spaces.

• The relation between polynomial decay and regularity of solutions in dispersive and dissipative equations.

• The study of dispersive blow-up of solutions.

• The study of Airy-type equations posed on metric graphs

In case you might be wondering how I ended up here...

For my undergraduate degree thesis, I worked with second order elliptic partial differential equations under the advisory of Prof. Carlos Augusto Vélez López. For my masters degree, in 2015 I started studying nonlinear dispersive equations. Under the advisory of Prof. José Manuel Jiménez Urrea I focused on the study of persistence of solutions in weighted Sobolev spaces for the so-called Korteweg-de Vries (KdV) equation. Even when a similar result for the KdV was already proven in 2015, I worked in an alternative way to obtain such theorem. 

In 2019 I started my PhD at Universidade Estadual de Campinas under the supervision of Prof. Ademir Pastor Ferreira. In the first year I started working with the same problem, but now for the 2D Zakharov-Kuznetsov (2D-ZK) from an article of my former M.Sc. advisor. When the 2020 pandemic arrived, the group of dispersive equations opened an online seminar in which many ideas came to my mind. In particular, a motivation to extend both: my master's degree thesis and the 2D-ZK work to a more general setting. A couple of months later, my first article related to local well-posedness of several dispersive equation took form. After some suggestions of my advisor, we applied the developed theory to the study of existence of disperive blow-up of solutions.

The natural continuation of the work already done began in late 2021 "after" the COVID19 pandemic. I started to think about the optimality of the relations displayed between the regularity and decay obtained in the first work. Such question I initially addressed it for the Kawahara equation and the Hirota-Satsuma system; obtaining only partial positive results. Once taking a close look the only result existing for the KdV equation, we adapted a slight improvement to the proof in the mKdV case which is currently submitted to peer review. 

Fortunately, many other topics end up being open for further research. I included some of them in the last chapter of my PhD thesis in case any of you wish to take a look. I am also open to discuss any of them.