GLOBAL-SOLUTIONS OF THE EQUATIONS OF ONE-DIMENSIONAL, COMPRESSIBLE FLOW WITH LARGE DATA AND FORCES, AND WITH DIFFERING END STATES

We prove the global existence of solutions of the Navier-Stokes equati ons of compressible flow in one space dimension with minimal hypothese s on the initial data, the equation of state, and the external force. Specifically, we require of the initial data only that the density be bounded above and below away from zero, and that the density and veloc ity be in L-2, module constant states at x = infinity and x = -infinit y, which may be different. There are no smallness hypotheses on either the data or on the external force. In particular, we include the impo rtant case that the initial data is piecewise constant with arbitraril y large jump discontinuities. Our results show that, even in this gene rality, neither vacuum states nor concentration states can form in fin ite time.