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Asymptotic behaviour of the density for one-dimensional Navier-Stokes equations. (English) Zbl 0687.35074

The paper addresses the question of global (in time) existence of a solution to the Navier-Stokes equation, for a barotropic (compressible) fluid, on a one-dimensional bounded domain.
The authors show that this problem has a global solution if the external force is time independent, moreover they show that the density is bounded away from zero below and bounded above provided that the external force and pressure satisfy a certain compatibility condition. This compatibility condition holds if the external force is sufficiently small. If this compatibility condition does not hold the density becomes zero or infinite asymptotically.
Reviewer: A.J.Meir

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B40 Asymptotic behavior of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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References:

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