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Harmonic Maps and Ideal Fluid Flows

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Author

Summary, in English

Using harmonic maps we provide an approach towards obtaining explicit solutions to the incompressible two-dimensional Euler equations. More precisely, the problem of finding all solutions which in Lagrangian variables (describing the particle paths of the flow) present a labelling by harmonic functions is reduced to solving an explicit nonlinear differential system in C-n with n = 3 or n = 4. While the general solution is not available in explicit form, structural properties of the system permit us to identify several families of explicit solutions.

Publishing year

2012

Language

English

Pages

479-513

Publication/Series

Archive for Rational Mechanics and Analysis

Volume

204

Issue

2

Document type

Journal article

Publisher

Springer

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 0003-9527