03-103 D. Cordoba, C. Fefferman, R. de la Llave

On squirt singularities (31K, LaTeX) Mar 10, 03

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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

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