scholarly journals On the Asymptotic Behavior of the Conjugate Problem Describing a Creeping Axisymmetric Thermocapillary Motion

2020 ◽  
pp. 26-36
Author(s):  
Victor K. Andreev ◽  
Evgeniy P. Magdenko
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Conjugate Problem ◽  
Cylinder Wall ◽  
Heat Conducting ◽  
Solid Cylinder ◽  
Viscous Heat ◽  
Initial Boundary Value ◽  
Heat Conducting Fluids ◽  
Creeping Motion

In this paper the conditions for the law of temperature behavior on a solid cylinder wall describes, under which the solution of a linear conjugate inverse initial-boundary value problem describing a two-layer axisymmetric creeping motion of viscous heat-conducting fluids tends to zero exponentially with increases of time

ASYMPTOTIC BEHAVIOR OF THE MOTION OF A VISCOUS HEAT-CONDUCTING ONE-DIMENSIONAL GAS WITH RADIATION: THE PURE SCATTERING CASE

2013 ◽  
Vol 11 (01) ◽  
pp. 1350003 ◽  
Author(s):  
BERNARD DUCOMET ◽  
ŠÁRKA NEČASOVÁ
Keyword(s):  
Large Time ◽  
Transport Coefficients ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Large Time Behavior ◽  
Heat Conducting ◽  
Time Behavior ◽  
Static State ◽  
Viscous Heat ◽  
Initial Boundary Value

We study the large-time behavior of the solution of an initial-boundary value problem for the equations of 1D motions of a compressible viscous heat-conducting gas coupled with radiation through a radiative transfer equation. Assuming only scattering processes between matter and photons (neglecting absorption and emission) and suitable hypotheses on the transport coefficients, we prove that the unique weak solution of the problem converges toward the static state.

The initial–boundary-value problem for real viscous heat-conducting flow with shear viscosity

2003 ◽  
Vol 133 (4) ◽  
pp. 969-986 ◽  
Author(s):  
Dehua Wang
Keyword(s):  
Initial Data ◽  
Boundary Value Problem ◽  
Shear Viscosity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
Large Initial Data ◽  
Viscous Heat ◽  
Initial Boundary Value

An initial–boundary-value problem for the nonlinear equations of real compressible viscous heat-conducting flow with general large initial data is investigated. The main point is to study the real flow for which the pressure and internal energy have nonlinear dependence on temperature, unlike the linear dependence for ideal flow, and the viscosity coefficients and heat conductivity are also functions of density and/or temperature. The shear viscosity is also presented. The existence, uniqueness and regularity of global solutions are established with large initial data in H1. It is shown that there is no shock wave, vacuum, mass concentration, or heat concentration (hot spots) developed in a finite time, although the solutions have large oscillations.

scholarly journals A Priori Estimates of the Conjugate Problem Describing an Axisymmetric Thermocapillary Motion for Small Marangoni Number

2019 ◽  
pp. 483-495 ◽  
Author(s):  
Victor K. Andreev ◽  
Evgeniy P. Magdenko
Keyword(s):  
A Priori Estimates ◽  
Solid Wall ◽  
A Priori ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Conjugate Problem ◽  
Point Of View ◽  
Heat Conducting ◽  
Priori Estimates ◽  
Viscous Heat

This paper is devoted to the study of equations solution describing the axisymmetric motion of a viscous heat-conducting liquid. The motion is interpreted as a two-layer flow of viscous heat-conducting liquids in a cylinder with a solid wall and a common movable non-deformable interface. From a mathematical point of view, the arising initial-boundary value problem is nonlinear and inverse. Under certain assumptions concerning to apply the problem is replaced by a linear one. As a result, the unimprovable uniform priori estimates for solutions of the problems posed are obtained

scholarly journals Filtration of Liquid in a Non-isothermal Viscous Porous Medium

2020 ◽  
pp. 763-773
Author(s):  
Alexander A. Papin ◽  
Margarita A. Tokareva ◽  
Rudolf A. Virts
Keyword(s):  
Porous Medium ◽  
Boundary Value Problem ◽  
Fluid Motion ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Heat Conducting ◽  
System Of Equations ◽  
One Dimensional ◽  
Unsteady Fluid ◽  
Initial Boundary Value

The solvability of the initial-boundary value problem is proved for the system of equations of one-dimensional unsteady fluid motion in a heat-conducting viscous porous medium

Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients

2019 ◽  
Vol 16 (03) ◽  
pp. 443-493 ◽  
Author(s):  
Yachun Li ◽  
Zhaoyang Shang
Keyword(s):  
Heat Conductivity ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Mhd Equations ◽  
Heat Conducting ◽  
Magnetic Diffusion ◽  
Viscosity Coefficients ◽  
Large Solutions ◽  
Mhd System ◽  
Initial Boundary Value

We consider the planar compressible magnetohydrodynamics (MHD) system for a viscous and heat-conducting ideal polytropic gas, when the viscosity, magnetic diffusion and heat conductivity depend on the specific volume [Formula: see text] and the temperature [Formula: see text]. For technical reasons, the viscosity coefficients, magnetic diffusion and heat conductivity are assumed to be proportional to [Formula: see text] where [Formula: see text] is a non-degenerate and smooth function satisfying some natural conditions. We prove the existence and uniqueness of the global-in-time classical solution to the initial-boundary value problem when general large initial data are prescribed and the exponent [Formula: see text] is sufficiently small. A similar result is also established for planar Hall-MHD equations.

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