# zbMATH — the first resource for mathematics

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

##### MSC:
 76T99 Multiphase and multicomponent flows 76E30 Nonlinear effects in hydrodynamic stability 76A02 Foundations of fluid mechanics
Full Text: