Non-implosion mechanism of 3D incompessible Euler equations

Abstract

This paper studies the non-implosion mechanism for the 3D incompressible Euler equations. We prove that vorticity blows up in finite time, whereas the $L^p_T L^\infty_{loc}$ $(p\in[1,\infty))$ norm of the velocity field remains bounded. Moreover, under an appropriate assumption on the scaling index, the exponent $p$ can be taken to be infinite. The proof is based on the introduction of a refined framework, the new observations for the null structure of transport term, and stability analysis of the self-similar model.