On two-dimensional gas expansion for pressure-gradient equations of Euler system ✩

In this paper we establish the existence of global continuous solutions of gas expansion into a vacuum for the two-dimensional pressure-gradient equations in gas dynamics. Under irrotational condition, By hodograph transformation, the flow is governed by the equation (p − p2 v)puu + 2pupvpuv + (p − p2u )pvv = 0, which can be further reduced to a inhomogeneous linearly degenerate system of three equations. Then the problem of the expansion of a wedge of gas into a vacuum is solved in the same way.  2004 Elsevier Inc. All rights reserved