Compact attractors for the Navier-Stokes equations of one-dimensional, compressible flow

We prove the existence of a compact attractor for the Navier-Stokes equatio ns of compressible fluid flow in one space dimension. We also show that the large-time behavior of a given solution is entirely determined by its valu es for all time at a finite number of points, given in terms of a certain d imensionless quantity associated with a canonical scaling of the system. Ou r results are based on a well-posedness theory for these equations which go es beyond previously known results. In particular, we establish the global existence and regularity of solutions with large external forces and large, nonsmooth initial data, with regularity estimates independent of time. (C) Academie des Sciences/Elsevier, Paris.