Global solution of an initial-value problem for two-dimensional compressible Euler equations
The author proves the existence of the unique global continuous solution for compressible Euler equations which describe an expansion of a gas wedge into vacuum. First, by hodograph transformation the governing quasi-stationary partial differential equations are reduced to a system of two inhomogeneous linearly degenerate equations in phase space under the condition that the flow is irrotational. Then the title problem is shown to be a uniformly hyperbolic Goursat-type problem for these two equations in the supersonic domain. A standard application of Gronwall's inequality implies the existence of the solution.
uniformly hyperbolic Goursat-type problem
scientific article; zbMATH DE number 1744188