The vanishing adiabatic exponent limits of Riemann solutions to the isentropic Euler equations for power law with a Coulomb-like friction term

Abstract

In this paper, we investigate the vanishing adiabatic exponent limits of the Riemann solutions to the isentropic Euler equations for power law with a Coulomb-like friction term. The formation of delta shock waves and vacuum states is identified and analyzed as the adiabatic exponent vanishes. Unlike the homogeneous case, the Riemann solutions are no longer self-similar. We rigorously justify that, as the adiabatic exponent vanishes, the Riemann solutions to the isentropic Euler equations for power law with a Coulomb-like friction term converge to the Riemann solutions to the zero pressure gas dynamics model with a body force. Moreover, we also give some numerical results to confirm the theoretical analysis.