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Global existence for a one-dimensional model in gas dynamics. (English) Zbl 0873.35070

Using an iterative procedure, the author proves the local existence of a solution for a system of equations describing an adiabatic one-dimensional flow of a viscous gas, taking into account the second gradient theory (and, as a consequence, the internal capillarity and the fourth-order viscosity coefficient). Because the capillarity coefficient provides regularity to the mass density, the author avoids the assumption that the initial data are small. In the particular case when the volume forces vanish, the application of a uniform Gronwall lemma gives the global existence of the solution.
Reviewer: O.Titow (Berlin)

MSC:

35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
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