  We discuss several approaches to generalized solutions of problems describing
the motion of inviscid fluids. We propose a new concept of dissipative solution
to the compressible Euler system based on a careful analysis of possible
oscillations and/or concentrations in the associated generating sequence.
Unlike the conventional measure-valued solutions or rather their expected
values, the dissipative solutions comply with a natural compatibility condition
- they are classical solutions as long as they enjoy certain degree of
smoothness.
