Abstract
We construct the equations for the incompressible two-fluid model of He(II). These equations provide a set of partial differential equations governing the thermomechanical behaviour of liquid helium below the λ-point. This set of equations is similar but slightly simpler than the equations originally proposed by Landau [1]. Following the standard approach of continuum mixture theory, we derive thermodynamic restrictions on the incompressible two-fluid model. Finally, we establish conditions which ensure that classical solutions of certain initial-boundary value problems for the simplified theory depend continuously on the initial data.
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