Abstract
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)|d2x 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.
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