- We prove the global existence of weak solutions to the Navier-Stokes equations for compressible, heat-conducting flow in one space dimension with large, discontinuous initial data, and we obtain a-priori estimates for these solutions which are independent of time, sufficient to determine their asymptotic behavior. In particular, we show that, as time goes to infinity, the solution tends to a constant state determined by the initial mass and the initial energy, and that the magnitudes of singularities in the solution decay to zero.
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Global solutions of the compressible Navier-Stokes equations with large discontinuous initial data
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