On Squirt Singularities in Hydrodynamics

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.

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