Finite speed propagation in the relaxation of vortex patches

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 | References | Similar Articles | Additional Information

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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DOI:
https://doi.org/10.1090/qam/1976366

Article copyright:
© Copyright 2003
American Mathematical Society