  We propose a two-dimensional generalization of Constantin-Lax-Majda model
[2]. Some results about singular solutions are given. This model might be the
first step toward the singular solutions of the Euler equations. Along the same
line (vorticity formulation), we present some further model equations. They
possibly models various aspects of difficulties related with the singular
solutions of the Euler and Navier-Stokes equations. We also make some
discussions on the possible connection between turbulence and the singular
solutions of the Navier-Stokes equations.
