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.
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Communicated by J. L. Lebowitz
Partly supported by Grant-in-Aid for Scientific Research No. B60460042, the Japan Ministry of Education, Science and Culture
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Giga, Y., Kambe, T. Large time behavior of the vorticity of two-dimensional viscous flow and its application to vortex formation. Commun.Math. Phys. 117, 549–568 (1988). https://doi.org/10.1007/BF01218384
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DOI: https://doi.org/10.1007/BF01218384