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Harmonic Maps and Ideal Fluid Flows

Aleman, Alexandru LU and Constantin, A. (2012) In Archive for Rational Mechanics and Analysis 204(2). p.479-513
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 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.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Archive for Rational Mechanics and Analysis
volume
204
issue
2
pages
479 - 513
publisher
Springer
external identifiers
  • wos:000302738000004
  • scopus:84859701974
ISSN
0003-9527
DOI
10.1007/s00205-011-0483-2
language
English
LU publication?
yes
id
267c8393-468a-4cb7-a121-fbaea3fc2ded (old id 2570871)
date added to LUP
2012-06-04 09:49:41
date last changed
2017-10-01 03:11:43
@article{267c8393-468a-4cb7-a121-fbaea3fc2ded,
  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 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.},
  author       = {Aleman, Alexandru and Constantin, A.},
  issn         = {0003-9527},
  language     = {eng},
  number       = {2},
  pages        = {479--513},
  publisher    = {Springer},
  series       = {Archive for Rational Mechanics and Analysis},
  title        = {Harmonic Maps and Ideal Fluid Flows},
  url          = {http://dx.doi.org/10.1007/s00205-011-0483-2},
  volume       = {204},
  year         = {2012},
}