Monge-Ampère Structures and the Geometry of Incompressible Flows
Monge-Ampère Structures and the Geometry of Incompressible Flows
We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Amp\`ere structure, and Burgers'-type vortices are a canonical class of solutions associated with this structure. The mapping of such solutions, which are characterised by a linear dependence of the third component …