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arXiv · 2310.05325

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

Gonzalo Cao-Labora·Javier Gómez-Serrano·Jia Shi·Gigliola Staffilani
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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, Rapha\"{e}l, Rodnianski, and Szeftel, Ann. of Math., 196(2):567-778, 2022, Ann. of Math., 196(2):779-889, 2022], [Buckmaster, Cao-Labora, and G\'{o}mez-Serrano, arXiv:2208.09445, 2022], but is flexible enough to handle both periodic and non-radial initial data.

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Gonzalo Cao-Labora, Javier Gómez-Serrano, Jia Shi, Gigliola Staffilani. 2023-10-09. Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$. https://arxiv.org/abs/2310.05325

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