The magnitude of the vorticity&ohgr;=|&ohgr;|for the3dincompressible Euler equations on the domain&OHgr;=[0,L]3with boundary conditionsun|∂&OHgr;=0is shown to satisfy the inequality‖log&ohgr;(t)‖2−‖log&ohgr;(0)‖2⩽∫0t‖&ohgr;(&tgr;)‖2 d&tgr;,for smooth initial data with no zeros in&ohgr;. The notation is‖&ohgr;‖22=∫&OHgr;&ohgr;2dVandtis time. The case when initial data have zeros in&ohgr;is also discussed. ©1997 American Institute of Physics.