Kuzmin-Oseledets formulations of compressible Euler equations case are considered. Exact results and physical interpretations are given. One such exact result for the compressible barotropic case is the potential helicity Lagrange invariant. In recognition of the fundamental physical implications of this Lagrange invariant clarified here, this invariant is shown to hold for compressible non-bar...

Optical Flow Methods for the Registration of Compressible Flow Images and Images Containing Large Voxel Displacements or Artifacts

We study the asymptotic behavior of compressible isentropic flow through porous medium with general L∞ initial data. The model system is the compressible Euler equation with frictional damping. As t → ∞, the density is conjectured to obey to the well-known porous medium equation and the momentum is expected to be formulated by Darcy’s law. Recent progress gives a definte answer to this conjectu...