On the Generalized Riemann Problem for compressible fluid flows: the three-dimensional case

The Generalized Riemann Problem (GRP) is considered for the compressible Euler equations in the three-dimensional formulation. The problem is stated as a Cauchy problem with initial data being smooth enough everywhere in space exept for a plane on which they have a discontinuity. The solution to the problem is represented with an asymptotic series in powers of a properly selected small parameter. The problem is solved for main (linear) terms of the expansion, which define the asymptotic behavior of the spatial GRP near the plane of initial discontinuity. It is shown that this solution is unique and can be obtained in an explicit analytical form for arbitrary initial data.