Mathematical Sciences

Lund University

Title Harmonic Maps and Ideal Fluid Flows
Authors Alexandru Aleman, A. Constantin
Alternative Location, Restricted Access
Publication Archive for Rational Mechanics and Analysis
Year 2012
Volume 204
Issue 2
Pages 479 - 513
Document type Article
Status Published
Quality controlled Yes
Language eng
Publisher Springer
Abstract 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.
ISBN/ISSN/Other ISSN: 0003-9527