Large time behavior of the vorticity of 2D viscous flow and vortex formation in 3D flow

We consider an initial value problem for the two-dimensional vorticity equation and show that the solution ω( x , t ) tends to Oseen's diffusing vortex at large times keeping the same total vorticity. No particular structure of the initial distribution ω( x ,0) is assumed except the restriction that R = (1/ν) f |( x , 0)| d 2 x is small. Applying a time-dependent scale transformation, we show the asymptotic stability of the Burgers' steady vortex. Physically this implies formation of a concentrated cylindrical vortex.