English

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

Analysis of PDEs 2025-04-22 v2 Mathematical Physics math.MP

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.

Keywords

Cite

@article{arxiv.2310.05325,
  title  = {Non-radial implosion for compressible Euler and Navier-Stokes in $\mathbb{T}^3$ and $\mathbb{R}^3$},
  author = {Gonzalo Cao-Labora and Javier Gómez-Serrano and Jia Shi and Gigliola Staffilani},
  journal= {arXiv preprint arXiv:2310.05325},
  year   = {2025}
}

Comments

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