The members of the Center for Research in Mathematical Engineering, CI²MA, Jéssika Camaño and Ricardo Oyarzúa -academicians of the Universidad Católica de la Santísima Concepción, UCSC, and the Universidad del Bío-Bío, UBB, respectively- visited the Department of Mathematics of the University of Trento in Italy to collaborate for two weeks with Professors Ana Alonso-Rodríguez and Alberto Valli, in the development of new mixed methods for magnetohydrodynamic equations.

The possibility of going to Italy to collaborate with these researchers arose when Camaño was developing her doctoral research. “They were my thesis co-advisors and, since then, we have been collaborating, so from that is where the connection to perform this research stay appears. In particular, this year, in January, in the context of Wonapde 2019 at the Universidad de Concepción, we talked with Ana about the possibility of starting to work on the problems that both of us were already addressing”, UCSC academician explains. The scientific challenges established by the four researchers come from magnetohydrodynamics field and describe the dynamics of electrically conductive fluids in the presence of electric and magnetic fields, Dr. Oyarzúa explains. “When Ana came earlier this year, we were starting to work on these equations, which correspond to a coupling of the Maxwell's equations, in which Ana is an expert, with the Navier-Stokes equations, in which Jessika and I have been working for a while. In fact, we already have something on the way with Carlos García, who graduated from the Doctorate program in applied sciences with major in Mathematical Engineering at UdeC and then performed a postdoctoral stay with me at UBB. So, we presented this mathematical problem to Ana who agreed to help us to improve it, through this stay we performed there”.

In addition, Dr. Camaño explains she also took the chance in this stay to address other research topics that she has been carrying out in collaboration with Dr. Alonso. “Some of the works that we are developing, and are still going on, deal with eigenvalue problems , so I also made progress in those studies with her”, she explains. The intention is that this be the beginning of a more fruitful future collaboration. “We have realized that, from what we have already done, a series of other works can be developed in the same direction. In addition, this allows that, eventually, some of our students could perform research stays in Trento”, Oyarzúa highlights. “We will continue collaborating in different lines related to electromagnetism. Although we made considerable progress, we still have to close things with them and, as we move forward in these studies, new research possibilities emerge, for example, by changing the perspective to address the proposed problems, which can generate new lines of work”, Camaño affirms.

This stay was funded by the Fondecyt projects led by Dr. Oyarzúa (1161325) and Dr. Camaño (1180859).