Physics

Isentropic process

Riemann hypothesis

Euler system

Mathematics

Logarithm

Euler's formula

Riemann's differential equation

Mathematical analysis

Roe solver

Riemann problem

Backward Euler method

Euler equations

Riemann Xi function

Equation of state

Semi-implicit Euler method

Thermodynamics

Mathematical Methods in the Applied Sciences

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.

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