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September 2022 On the implosion of a compressible fluid II: Singularity formation
Frank Merle, Pierre Raphaël, Igor Rodnianski, Jeremie Szeftel
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Ann. of Math. (2) 196(2): 779-889 (September 2022). DOI: 10.4007/annals.2022.196.2.4

Abstract

In this paper, which continues our investigation of strong singularity formation in compressible fluids, we consider the compressible three-dimensional Navier-Stokes and Euler equations. In a suitable regime of barotropic laws, we construct a set of finite energy smooth initial data for which the corresponding solutions to both equations implode (with infinite density) at a later time at a point, and completely describe the associated formation of singularity. An essential step in the proof is the existence of $\mathcal{C}^\infty$ smooth self-similar solutions to the compressible Euler equations for quantized values of the speed constructed in our companion paper (part I). All blow up dynamics obtained for the Navier-Stokes problem are of type II (non self-similar).

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Frank Merle. Pierre Raphaël. Igor Rodnianski. Jeremie Szeftel. "On the implosion of a compressible fluid II: Singularity formation." Ann. of Math. (2) 196 (2) 779 - 889, September 2022. https://doi.org/10.4007/annals.2022.196.2.4

Information

Published: September 2022
First available in Project Euclid: 28 June 2022

Digital Object Identifier: 10.4007/annals.2022.196.2.4

Subjects:
Primary: 35B44 , 35Q35

Keywords: compressible fluids , singularity formation

Rights: Copyright © 2022 Department of Mathematics, Princeton University

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Vol.196 • No. 2 • September 2022
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