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\(L^ 1\) asymptotic behavior of compressible, isentropic, viscous 1-D flow. (English) Zbl 0807.35110
We study the large time behavior in \(L^ 1\) of the compressible, isentropic, viscous 1-D flow. Under the assumption that the initial data are smooth and small, we show that the solutions are approximated by the solutions of a parabolic system, and in turn by diffusion waves, which are solutions of Burgers equations. Decay rates in \(L^ 1\) are obtained. Our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system.

MSC:
35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
35L65 Hyperbolic conservation laws
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