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On the structure of equilibrium phase transitions within the gradient theory of fluids. (English) Zbl 0665.76120
The stable density distributions u of a two-phase fluid are studied in the case when the free-energy (per unit volume) has the form: \(W(u(x))+\sigma | \nabla u(x)|^ 2\). Usually the corresponding minimizers are piecewise-constant functions with an arbitrary number of transitions. Here it is proved that the term \(\sigma | \nabla u(x)|^ 2\) rules out such complicated behaviour, at least for (non- circular) cylinders or for regions with rotational symmetries. Some of the results are valid for any stationary point of the total energy.
Reviewer: D.Polisevski

76T99 Multiphase and multicomponent flows
76E30 Nonlinear effects in hydrodynamic stability
76A02 Foundations of fluid mechanics
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