The limit behavior of Riemann solutions to the Euler equations of compressible fluid flow for the modified Chaplygin gas

In this paper, we study the formation of delta shock waves and vacuum states in a pressureless limit of solutions to the Euler equations of compressible fluid flow for modified Chaplygin gas as two parameters tend to zero. At first, the Riemann problem of Euler equations of compressible fluid flow for modified Chaplygin gas is solved. Then, as the pressure drops to zero, we strictly confirm that the two-shock Riemann solution converges to a delta shock wave solution and the two-rarefaction wave Riemann solution converges to a two-contact discontinuity solution with the intermediate state approaching a vacuum state. At last, some numerical simulations are given to verify the above analysis.