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

AbstractIn 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−p2v)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