Abstract
This thesis is a survey of research result of Giga and Kambe on the vorticity equation. In this thesis, we start with the Navier-Stokes equations, which describe the incompressible viscous flows in fluid mechanics, then the vorticity equation is derived from them. Based on the existence and uniqueness for the solution of the vorticity equation, we have the asymptotic formula for the solution which means the solution will approach the fundamental solution of the heat equation as time is large enough. Then we discuss an application of this asymptotic formula.