Energy-minimising parallel flows  with prescribed vorticity distribution

J. F. Toland

doi:10.3934/dcds.2014.34.3193

Article Contents

2014, Volume 34, Issue 8: 3193-3210. Doi: 10.3934/dcds.2014.34.3193

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Energy-minimising parallel flows with prescribed vorticity distribution

J. F. Toland^1,

1.
St John's College, Cambridge, CB2 1TP

Received: March 31, 2013

Published: July 2014

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Abstract

This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by other constraints. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler's equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

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Mathematics Subject Classification: 76B15, 35C07, 49K30.

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