On squirt singularities in hydrodynamics

Diego Córdoba, Charles Fefferman, Rafael De La Llave

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


We consider certain singularities of hydrodynamic equations that have been proposed in the literature. We present a kinematic argument that shows that if a volume preserving field presents these singularities, certain integrals related to the vector field have to diverge. We also show that if the vector fields satisfy certain partial differential equations (Navier-Stokes, Boussinesq), then the integrals have to be finite. As a consequence, these singularities are absent in the solutions of the above equations.

Original languageEnglish (US)
Pages (from-to)204-213
Number of pages10
JournalSIAM Journal on Mathematical Analysis
Issue number1
StatePublished - 2005

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Analysis
  • Applied Mathematics


  • Boussinesq equations
  • Navier-Stokes equations
  • Singularities


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