For gas dynamics equations such as compressible Euler and Navier-Stokes equations, preserving the positivity of density and pressure without losing conservation is crucial to stabilize the numerical computation.

In image and audio signal classification, a major problem is to build stable representations that are invariant under rigid motions and, more generally, to small diffeomorphisms. Translation invariant representations of signals in Cn are of particular importance.

In the study of an isolated vortex line for 3D Euler one is trying to make sense of the evolution of a curve, where the vorticity (a distribution in this case) is supported, and tangential to the curve.  This idealised vorticity generates a velocity field that is too singular (like the inverse of th