Finite-time blowup of the Euler equation without forcing

Abstract

These notes present the construction in \cite{euler} of finite-time blowup for the three-dimensional incompressible, unforced Euler equations on ${\mathbb{R}}^3$: \begin{equation} \partial_tu+(u\cdot\nabla)u+\nabla p=0,\qquad \nabla\cdot u=0. \end{equation} The construction successively adds oscillatory layers to smooth parent solutions. Each layer is constructed by a finite expansion and an exact correction, so that the resulting child solves Euler.

arXiv comment107 pages