International experts discuss the latest advances in the Mathematics of fluids
19 June 2026
International researchers gathered at CUNEF Universidad and the Institute of Mathematical Sciences (ICMAT) for the conference “Modern Perspectives on the Mathematics of Fluids”. The event aimed to deepen understanding of fluid behavior, bringing together scholars from prestigious institutions such as the California Institute of Technology, ETH Zürich, and Princeton University.
Participants had the opportunity to exchange ideas on the theory of partial differential equations (PDEs) applied to the Euler and Navier - Stokes equations, as well as on modern analytical techniques including convex integration, compensated compactness, and spectral and semigroup methods.
The sessions, organized by ICMAT-CSIC research professors Diego Córdoba, Alberto Enciso, and Daniel Peralta-Salas, together with CUNEF Universidad Mathematics Department professors Óscar Domínguez and Luis Martínez-Zoroa, focused on the presentation of ongoing research and the discussions generated among participants.
Research Highlights
During the conference, experts explored questions such as the main factors that explain the formation of vortices in the oceans and the atmosphere, and whether a wave can undergo breaking in finite time starting from smooth initial conditions. In this context, participants examined in greater depth how the dynamics of incompressible fluids, such as water and low-speed air, are described by the Euler and Navier–Stokes equations. Although these equations were formulated in the eighteenth and nineteenth centuries, respectively, their mathematical understanding remains far from complete.
As the experts discussed, determining whether solutions to the Navier–Stokes equations can develop singularities, that is, whether certain quantities such as velocity or its derivatives can become infinite in finite time, continues to be one of the major open problems in mathematics. This question is one of the seven Millennium Prize Problems established by the Clay Mathematics Institute, the solution of which carries a prize of one million dollars.
The organization of this international conference further strengthens CUNEF Universidad role in the mathematical analysis of partial differential equations and fluid mechanics, consolidating its position as one of the leading international centers for research in these fields.
