Global stability of solutions with discontinuous initial data containing vacuum states for the isentropic Euler equations (Q1880226)

The paper deals with the global stability of entropy solutions in \(L^\infty\) containing vacuum states for the isentropic Euler equations \[ \partial_t\rho+\partial_x m=0,\qquad \partial_t m+\partial_x(m^2/\rho+p(\rho))=0, \] where \(\rho, m,\) and \(p\) represent the density, the mass, and the pressure, respectively, and are in the physical region \[ \{(\rho,m)\; : \;\rho\geq 0,\;| m/\rho| \leq C_0\} \] for some \(C_0>0.\) The uniqueness of Lipschitz solutions with discontinuous initial data is obtained in the broad class of entropy solutions in \(L^\infty\) containing vacuum states.