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

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 [51, 52, 8], but is flexible enough to handle both periodic and non-radial initial data.

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Publication Details

Journal
Cambridge Journal of Mathematics
Published
2026-01-01
DOI
https://doi.org/10.4310/cjm.260107044458
Primary Topic
Navier-Stokes equation solutions
Type
article
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article

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

Gigliola Staffilani, J. Shi, G. Cao-Labora, J. Gómez-Serrano
Cambridge Journal of Mathematics
Navier-Stokes equation solutions
article

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

Gigliola Staffilani, J. Shi, G. Cao-Labora, J. Gómez-Serrano
article en

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 [51, 52, 8], but is flexible enough to handle both periodic and non-radial initial data.

Cambridge Journal of MathematicsVol. 13(4)
Institute for Advanced Study (US), Indiana University Bloomington (US), École Polytechnique Fédérale de Lausanne (CH), Massachusetts Institute of Technology (US)
Openalex Percentile: Top 94%
Navier-Stokes equation solutions
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