Abstract: Barotropic Euler equations are a particular case of Jacobi type systems, which have a geometrical representation in terms of differential 2-forms on 0-jet space. This observation naturally leads to the notion of a generalized (multivalued) solution of Euler equations understood as an integral manifold of the mentioned forms. We combine this observation with adding a differential constraint to the original system in such a way that integration can be performed explicitly. We will discuss two ways of finding such constraints: in one of them, the mentioned specific geometry of barotropic Euler equations is used, while another one is based on differential invariants of their symmetry group and quotient PDEs. Finally, we will show how all these ideas make it possible to find solutions with singularities.
Organiser: David Cohen (email@example.com). Please contact me if you need the Zoom password.