On Self-similar Solutions to Degenerate Compressible Navier–Stokes Equations

Pierre Germain, Tsukasa Iwabuchi, Tristan Léger

Research output: Contribution to journalArticlepeer-review


We study cavitating solutions to compressible Navier–Stokes equations with degenerate density-dependent viscosity. We consider two types of small radial solutions: forward self-similar (expanders), and backward self-similar (shrinkers). In the first case, we construct such solutions by a fixed-point argument. In the second case, we prove non-existence of such solutions using weighted energy estimates.

Original languageEnglish (US)
Pages (from-to)1001-1030
Number of pages30
JournalCommunications In Mathematical Physics
Issue number3
StatePublished - Feb 2021

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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