The limiting behavior of the Riemann solution to the isentropic Euler system for logarithmic equation of state with a source term

We investigate the limiting behavior of the Riemann solution to the isentropic Euler equations for logarithmic equation of state with the Coulomb‐like friction term. The formation of vacuum state and delta shock waves are identified and analyzed when the pressure vanishes. Unlike the homogeneous case, the Riemann solution is no longer self‐similar. We prove that the Riemann solution of the isentropic Euler equations for logarithmic equation of state with friction term converges to the Riemann solution of the zero‐pressure gas dynamics system with a body force when the pressure vanishes.