TITLE

Harmonic Maps and Ideal Fluid Flows

AUTHOR(S)
Aleman, A.; Constantin, A.
PUB. DATE
May 2012
SOURCE
Archive for Rational Mechanics & Analysis;May2012, Vol. 204 Issue 2, p479
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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 $${\mathbb {C^n}}$$ 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.
ACCESSION #
74188056

 

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