Diego Córdoba

Diego Córdoba is a Spanish mathematician known for his work on fluid dynamics equations, particularly the Euler and Navier–Stokes equations. Together with co-authors, he proved the possibility of finite-time blow-up for the three-dimensional Euler equations with an external force and for the porous medium equation. His constructions, based on smoothing and the use of special profiles, became an important step toward understanding singularities in incompressible fluids. These results are often seen as precursors to later numerical and analytical work, including recent research by OpenAI, where blow-up is achieved with a smooth force. Córdoba showed that even in the absence of viscosity, one can construct solutions that break down in finite time if a sufficiently regular external forcing is allowed.

Biography

Diego Córdoba was born in 1971. He was educated in Spain, earning his PhD at the Complutense University of Madrid. He worked at various research centers, including Princeton University and the University of Chicago, before returning to Spain. He is currently a professor at the Institute of Mathematical Sciences (ICMAT) in Madrid. He has collaborated with mathematicians such as Antonio Córdoba, Charles Fefferman, and others. He is a recipient of several Spanish scientific awards.

Key discoveries

Proof of finite-time blow-up for the three-dimensional Euler equations with an external force (jointly with Martínez-Zoroa et al.).
Study of the porous medium equation and its singular solutions.
Development of methods for constructing solutions with loss of regularity in fluid dynamics, which were later adapted in numerical experiments.

Biography

Key discoveries

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