An initial boundary value problem for systems of viscous two-fluid media with equilibrium of pressure phases is considered. Using the test function method proposed by S.I. Pohozhaev and E. Mitidieri, the effect of boundary and initial conditions on the appearance, time and rate of destruction of solutions of this problem...

A system of the Burgers equations of the two-velocity hydrodynamics is obtained. We consider the Cauchy problem in the case of a one-dimensional system. The estimate of the stability of the solution is obtained. We have obtained a formula for the Cauchy problem for the one-dimensional system of equations that...

A series of the differential identities connecting velocities, pressure and body force in the two-velocity hydrodynamics equations with equilibrium of pressure phases are found. Some of these identities have a divergent form and can be considered to be certain conservation laws. It is detected that the flow functions for the...

A flow of incompressible viscous two-velocity fluids for the case of pressure equilibrium of phases at constant saturation of substances is described with the help of scalar functions. A system of differential equations for these functions is obtained. An example illustrating this method is presented.

The fundamental solution to describe the three-dimensional steady-state flows of viscous fluids of the two-velocity continuum with pressure phase equilibrium has been obtained.