On the implosion of a compressible fluid II:Singularity formation

Frank Merle, Pierre Raphaël, Igor Rodnianski, Jeremie Szeftel

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


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 (Formula Presented) smooth selfsimilar solutions to the compressible Euler equations for quantized values of the speed constructed in our companion paper (part I).

Original languageEnglish (US)
Pages (from-to)779-889
Number of pages111
JournalAnnals of Mathematics
Issue number2
StatePublished - Sep 2022

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)


  • Compressible fluids
  • Singularity formation


Dive into the research topics of 'On the implosion of a compressible fluid II:Singularity formation'. Together they form a unique fingerprint.

Cite this