D. Cordoba, C. Fefferman, R. de la Llave
On squirt singularities
(31K, LaTeX)
ABSTRACT. 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 equations. This answers a question posed by K. Moffatt
in R.L. Ricca(ed.) {\sl An introduction to the geometry and topology of
fluid flows}, Kluwer 2001