Some new exact solutions for the two-dimensional Navier-Stokes equations

In this Letter, under the precondition that the fluid movement satisfies the law of mass conservation, a two-dimensional Hopf-Cole transformation with mass conservation (2D Hopf-Cole transformation) is established. On the basis of 2D Hopf-Cole transformation, three exact solutions of two-dimensional Navier-Stokes equations (2D N-S equations) are presented. Some physical properties of the exact solutions of 2D N-S equations are described preliminarily.