Related papers: A general existence result for isothermal two-phas…
In the framework of the thermodynamic perturbation theory for fluids we study how the phase diagram of an isotropic repulsive soft-core attractive potential, where a liquid-liquid phase transition exists in addition to the standard…
We consider the gauge transformations of a metric $G$-bundle over a compact Riemannian surface with boundary. By employing the heat flow method, the local existence and the long time existence of generalized solution are proved.
Our study of a basic model for incompressible two-phase flows with phase transitions consistent with thermodynamics in the case of constant but non-equal densities of the phases, begun by the first two authors is continued. We extend our…
The piston problem, i.e. the dynamics in a uniform gas at rest under the action of a moving piston is fundamental problem of physics and a canonical case study in shock wave physics. We investigate theoretically and experimentally the…
Gas injection in the context of the three-phase flow in porous media appears in applications such as Enhanced Oil Recovery, aquifer remediation, and carbon capture, utilization, and storage (CCUS). In general, this technique suffers from a…
In this paper, we consider Riemann solvers with phase transition effects based on the Euler-Fourier equation system. One exact and two approximate solutions of the two-phase Riemann problem are obtained by modelling the phase transition…
The solution of a momentum conservation equation for the gas and liquid stream in the flowing element is obtained on the basis of the modern approach to a problem on contact interaction of bodies and mediums. A flowing element, system are:…
This work focuses on the Riemann problem of Euler equations with global constant initial conditions and a single-point heating source, which comes from the physical problem of heating one-dimensional inviscid compressible constant flow. In…
In this paper the motion of two-phase, incompressible, viscous fluids with surface tension is investigated. Three cases are considered: (1) the case of heat-conducting fluids, (2) the case of isothermal fluids, and (3) the case of Stokes…
We set up and study a coupled problem on stationary non-isothermal flow of electrorheological fluids. The problem consist in finding functions of velocity, pressure and temperature which satisfy the motion equations, the condition of…
Consider the (simplified) Leslie-Erickson model for the flow of nematic liquid crystals in a bounded domain $\Omega \subset \mathbb{R}^n$ for n > 1$. This article develops a complete dynamic theory for these equations, analyzing the system…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
In this paper we consider the equation system describing the motion of the air and the variation of the radiation intensity and the quantity of water droplets in the air, including also the process of water phase transition. Under a…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
We study the existence and properties of Lipschitz continuous weak solutions to the Neumann boundary value problem for a class of one-dimensional quasilinear forward-backward diffusion equations with linear convection and reaction. The…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the…
We investigate a new diffuse-interface model that describes creeping two-phase flows (i.e., flows exhibiting a low Reynolds number), especially flows that permeate a porous medium. The system of equations consists of a Brinkman equation for…
The generalized method of characteristics is used to obtain rank-2 solutions of the classical equations of hydrodynamics in (3+1) dimensions describing the motion of a fluid medium in the presence of gravitational and Coriolis forces. We…