Vladimir Shelukhin

Vanishing shear viscosity in the equations of compressible fluids for the flows with the cylinder symmetry

We analyze the question of the limit process when the shear viscosity goes to zero for global solutions to the Navier--Stokes equations for compressible heat conductive fluids for the flows which are invariant over cylindrical sheets.

A quasi-linear parabolic system for three-phase capillary flow in porous media

A parabolic system is proposed to describe three-phase capillary flows in porous media. The assumptions imposed on the phase interaction mean that the capillarity matrix is triangular. The unique solvability of an associated nondegenerate parabolic system is proved for the Cauchy problem in a class of x-periodic solutions.

Initial Boundary Value Problems for a Quasi-linear Parabolic System in Three-Phase Capillary Flow in Porous Media

We study two types of initial boundary value problems for a quasi-linear parabolic system motivated by three-phase flows in porous media in the presence of capillarity effects. The first type of problem prescribes a mixed boundary condition, involving a combination of the value of the solution and its normal derivative at the boundary. The second type prescribes the value of the solution at the boundary, which is the so-called Dirichlet boundary condition. We prove the existence and uniqueness of smooth solution for the first type of initial boundary value problem, and we obtain the existence of a solution for the second one as a limit case of the first type. The main assumption about the diffusion matrix of the system is that it is triangular with strictly positive diagonal elements. Another interesting feature is concerned specifically with the application to three-phase capillary flow in a porous medium. Namely, we derive an important practical consequence of the assumption that the capillarity matrix ...

Global Weak Solutions to Equations of Compressible Miscible Flows in Porous Media

We study the one‐dimensional equations governing compressible flows of m miscible components in a porous medium. The equations are reduced to a quasi‐linear parabolic system for the discharge function P and the concentrations

Homogenization of the Poisson—Boltzmann Equation

c_i

Boundary Layers for the Navier–Stokes Equations¶of Compressible Fluids

. The equations of this system are strongly coupled since the parabolic equation for

Electroosmosis law via homogenization of electrolyte flow equations in porous media

c_i

Nonhomogeneous Incompressible Herschel–Bulkley Fluid Flows Between Two Eccentric Cylinders

contains both the second derivative

Homogenization of time harmonic Maxwell equations and the frequency dispersion effect

c_{ixx}

Global Solvability of the One-Dimensional Cosserat–Bingham Fluid Equations

and the second derivative