Global existence of solutions to system of polytropic gas dynamics with friction (Q1681028)

The author considers the global existence problem for weak solutions to the Cauchy problem for a 1D system of polytropic gas dynamics in a divergent nozzle with friction. Initial data are \(L^\infty\)-bounded. The nozzle is axisymmetrical and described by the cross-section area \(a(x)\) at a point \(x\). The author applies the maximum principle to obtain a uniformly bounded \(L^\infty\) estimation and the compensated compactness to prove the convergence of approximations and thus the global existence of entropy solutions.