Non-radial implosion for compressible Euler and Navier-Stokes in ${\mathbb{T}}^3$ and ${\mathbb{R}}^3$

Abstract

In this paper we construct smooth, non-radial solutions of the compressible Euler and Navier-Stokes equation that develop an imploding finite time singularity. Our construction is motivated by the works [Merle, Raphaël, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022], [Buckmaster, Cao-Labora, and Gómez-Serrano, arXiv:2208.09445, 2022], but is flexible enough to handle both periodic and non-radial initial data.

80 pages, 6 figures. To appear in Cambridge Journal of Mathematics