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In this paper we derive kinematic relations for quantities involving the rateof strain tensor and the Hessian of the pressure for solutions of the 3D Eulerequations and the 2D Boussinesq equations. Using these kinematic relations, weprove new blow up criteria and obtain conditions for the absence of type Isingularity for these equations. We obtain both global and localized versionsof the results. Some of the new blow up criteria and type I conditions improveprevious results of [3].

Remarks on type I blow up for the 3D Euler equations and the 2D Boussinesq equations