||Harmonic Maps and Ideal Fluid Flows
||http://dx.doi.org/10.1007/s..., Restricted Access
||Archive for Rational Mechanics and Analysis
||479 - 513
||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.