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Attracteurs compacts pour les équations de Navier-Stokes d’un fluide compressible monodimensionel. (Compact attractors for the Navier-Stokes equations of one-dimensional, compresible flow.) (English. Abridged French version) Zbl 0926.35113
Summary: We prove the existence of a compact attractor for the Navier-Stokes equations 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 values for all time at a finite number of points, given in terms of a certain dimensionless quantity associated with a canonical scaling of the system. Our results are based on a well-posedness theory for these equations which goes 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.

MSC:
35Q30 Navier-Stokes equations
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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