Exact steady solutions of the three-dimensional gas dynamics equations

This paper investigates the three-dimensional stationary gas dynamic equations for an ideal adiabatic gas and employs symmetry-based methods to construct exact analytical solutions. In the Chaplygin gas case, the analysis produces a remarkably general family of solutions depending on three arbitrary functions, whereas for a general adiabatic index the equations admit several classes of explicit solutions parameterized by a finite set of constant parameters.