Multidimensional Shock Interaction for a Chaplygin Gas

A Chaplygin gas is an inviscid, compressible fluid in which the acoustic fields are linearly degenerate. We analyze the multidimensional shocks in such a fluid, which turn out to be sonic. Two shocks in general position interact rather simply. We investigate several two-dimensional Riemann problems and prove the existence of a unique solution. Among them is the supersonic reflection of a planar shock against a wedge; we remark that the solution cannot be a Mach reflection, contrary to what happens for other gases, and that there always exists a solution in the form of a regular reflection.