40:48
published on May 21, 2026
Jumps, cusps and fractals in the solution of dispersive equations
By Beatrice Pelloni
2D flows with random initial vorticity
Appears in collection : 2026 - T2 - WS1 - Vortices and vorticity in geophysical flows
We consider a random initial vorticity $\omega_0(x) = \sum_{n\in \mathbb{Z}^2} a_n \phi(x-n)$, where $\phi$ is bounded and compactly supported and {a_n} are independent, uniformly bounded, mean $0$, variance $1$ random variables (in other words, $\omega_0$ is an array of randomly weighted vortex blobs). We prove global well-posedness of weak solutions to the Euler equations in $\mathbb{R}^2$ for almost every such initial vorticity.
