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Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation

Research paper by Yoshikazu Giga, Tsutomu Kambe

Indexed on: 01 Dec '88Published on: 01 Dec '88Published in: Communications in Mathematical Physics



Abstract

We consider the Cauchy problem for the two-dimensional vorticity equation. We show that the solution ω behaves like a constant multiple of the Gauss kernel having the same total vorticity as time tends to infinity. No particular structure of initial data ω0=ω(x, 0) is assumed except the restriction that the Reynolds numberR=∝|ω0|dx/v is small, wherev is the kinematic viscosity. Applying a time-dependent scale transformation, we show a stability of Burgers' vortex, which physically implies formation of a concentrated vortex.