A simplified two-fluid theory for helium(II)

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 ?-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. © 1976.