Abstract: In this paper, we mainly study the two-dimensional Riemann problem of irrotational initially and isentropic Chaplygin gas with four piecewise constants. And we obtain the existence of the classical weak solution under the conditions on the large initial data. By using the generalized characteristic analysis method, we consider the situation that the initial discontinuities conduce to six elementary waves. Then we classify the structures constructed by these elementary waves. Moreover we get the necessary and sufficient conditions for the classical weak solutions of two representative wave structures for which we construct the piecewise smooth solutions.

Key words: Chaplygin gas, Two-dimensional Riemann problem, Wave interaction