Speaker: Diego Córdoba dell'Instituto de Ciencias Matemáticas (ICMat-CSIC), Spagna
State of the Art in Finite-Time Singularities for the 3D Incompressible Euler Equations
The Euler equations have long been a central model in incompressible fluid dynamics. One of the most fundamental open problems in their mathematical theory is whether solutions can develop singularities in finite time, a question that has remained unresolved since Euler’s original work in 1757.
In recent years, significant progress has been made toward understanding possible blow-up scenarios through increasingly refined analytical mechanisms. Among these, a novel framework has emerged based on a cascade of vorticity concentrated at progressively smaller spatial scales, leading to an uncontrolled growth of velocity derivatives in finite time. This approach has made it possible to construct the most regular solutions known to date that nonetheless exhibit singular behavior in finite time.
Where: Accademia delle Scienze detta dei XL a villa Torlonia
