Vanishing pressure in gas dynamics equations (Q1975498)

The authors examine a specific one-dimensional degenerate hyperbolic system \(\rho_t+(\rho u)_x= 0\), \((\rho u)_t+ (\rho u^2/2)_x= 0\), which can describe the dynamics of galaxies (the so-called zero pressure gas dynamics). The solutions are obtained from the usual gasdynamic equations by multiplying pressure by a small number \(\varepsilon\) and passing to the limit as \(\varepsilon\) vanishes. The convergence proof is restricted to regular solutions, and is based on the use of Riemann invariants.