On the blow-up of solutions of the 3-D Euler equations in a bounded domain

It is shown that if 0, ) is the maximal interval of existence of a smooth solutionu of the incompressible Euler equations in a bounded, simply connected domain R ³, then , where =×u is the vorticity. Crucial to this result is a special estimate proven in of the maximum velocity gradient in terms of the maximum vorticity and a logarithmic term involving a higher norm of the vorticity.