Finite speed propagation in the relaxation of vortex patches

Rosier, Carole; Rosier, Lionel

doi:10.1090/qam/1976366

Authors: Carole Rosier and Lionel Rosier
Journal: Quart. Appl. Math. 61 (2003), 213-231
MSC: Primary 76B47; Secondary 35K65, 35Q30, 76F99
DOI: https://doi.org/10.1090/qam/1976366
MathSciNet review: MR1976366
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Abstract: A degenerate parabolic equation has been proposed by Robert and Sommeria to describe the relaxation towards a statistical equilibrium state for a two-dimensional incompressible perfect fluid with a vortex patch as initial vorticity. In this paper, flows obtained by numerical integration of the Robert-Sommeria equation over a long-time interval are compared with those obtained for the Navier-Stokes equation at high Reynolds number. A finite speed propagation for the extremal values of the vorticity is numerically shown to hold for the Robert-Sommeria equation. A rigorous proof of this (fine) property is also provided.

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