  In this paper we derive kinematic relations for quantities involving the rate
of strain tensor and the Hessian of the pressure for solutions of the 3D Euler
equations and the 2D Boussinesq equations. Using these kinematic relations, we
prove new blow up criteria and obtain conditions for the absence of type I
singularity for these equations. We obtain both global and localized versions
of the results. Some of the new blow up criteria and type I conditions improve
previous results of [3].
