Well-posedness of the equations of a non-homogeneous perfect fluid

Marsden, J. E.

Comm. Partial Differential Equations, 1, (1976), 215-230

Abstract:

The Euler equations for a non-homogeneous, non-viscous compressible fluid are shown to be well-posed for a short time interval, using techniques of infinite dimensional geometry and a weighted Hodge theorem. Regularity and other properties of these solutions are pointed out as well.