THE CONVERGENCE IN WEAK TOPOLOGIES OF APPROXIMATE METHODS FOR AN ISENTROPIC GAS-DYNAMIC SYSTEM

The Cauchy problem for an isentropic gas-dynamic system is considered. Theorems on the convergence of the viscosity and smoothing methods are established. It is proved that subsequences of approximate solutions converge to a functional solution of the initial-value Cauchy problem in weak topologies by means of uniform estimates of the approximate solutions in L1(loc) and L2(loc). The discrepancies of the methods are estimated.