Global Existence and Exponential Stability for a Real Viscous Heat-conducting Flow with Shear Viscosity

2012 ◽  
pp. 33-74
Author(s):  
Yuming Qin ◽  
Lan Huang
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Shear Viscosity ◽  
Heat Conducting ◽  
Viscous Heat

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.

Spin down problem of rotating stratified fluid in thermally insulated circular cylinders

1969 ◽  
Vol 37 (4) ◽  
pp. 689-699 ◽  
Author(s):  
Takeo Sakurai
Keyword(s):  
Steady State ◽  
Time Scale ◽  
Boussinesq Approximation ◽  
Circular Cylinders ◽  
Heat Conducting ◽  
Quasi Steady State ◽  
Homogeneous Fluid ◽  
Time Duration ◽  
Viscous Heat ◽  
Final Approach

A response of viscous heat-conducting compressible fluid to an abrupt change of angular velocity of a containing thermally insulated circular cylinder under the existence of stable distribution of the temperature is investigated within the framework of the Boussinesq approximation for a time duration of the order of the homogeneous-fluid spin down time in order to resolve the Holton-Pedlosky controversy. The explicit expression of the solution is obtained by the standard method and Holton's conclusion is confirmed. The secondary meridional current induced by the Ekman layers spins the fluid down to a quasi-steady state within the present time scale. However, unlike the homogeneous case, the quasi-steady state is not one of solid body rotation. The final approach to the state of rigid rotation is achieved via the viscous diffusion in the time scale of the usual diffusion time.

scholarly journals On the System of Coupled Nondegenerate Kirchhoff Equations with Distributed Delay: Global Existence and Exponential Decay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Abdelbaki Choucha ◽  
Salah Mahmoud Boulaaras ◽  
Djamel Ouchenane ◽  
Salem Alkhalaf ◽  
Ibrahim Mekawy ◽  
...  
Keyword(s):  
Global Existence ◽  
Exponential Stability ◽  
Galerkin Method ◽  
Exponential Decay ◽  
Energy Method ◽  
Existence Of Solutions ◽  
Distributed Delay ◽  
Stability Result ◽  
Kirchhoff Equations ◽  
Global Existence Of Solutions

This paper studies the system of coupled nondegenerate viscoelastic Kirchhoff equations with a distributed delay. By using the energy method and Faedo-Galerkin method, we prove the global existence of solutions. Furthermore, we prove the exponential stability result.

scholarly journals MATHEMATICAL MODELING AND CALCULATION OF GAS DYNAMIC CHARACTERISTICS OF FREE THERMAL AIR VORTEX

2017 ◽  
pp. 93-98
Author(s):  
D. D. Barannikova ◽  
A. G. Obukhov
Keyword(s):  
Gas Flow ◽  
Local Heating ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Point Of View ◽  
Underlying Surface ◽  
Heat Conducting ◽  
Gas Dynamics Equations ◽  
Viscous Heat ◽  
Flow Formation

The article analyzes experimental and analytical studies of ascending swirling air flows. In experimental works such flows are considered from the point of view of the direction of twist, the thermal regimes of heating the underlying surface, the estimation of integral parameters, the method of influence on them, and various methods of visualization. In analytical papers, by constructing solutions of the system of gas dynamics equations, the emergence of a twist of the corresponding direction is proven when there is a gas flow into a vertical cylinder of nonzero radius. In addition, in the numerical modeling of thermal ascending swirling flows, a feature was observed in the behavior of a moving gas at the initial moments of flow formation when the underlying surface was heated locally. This feature consists in the appearance on the boundary of the heating region of counter propagating gas flows with opposite directions of twist. The paper presents the results of numerical simulation of three-dimensional unsteady flows of a compressible viscous heat-conducting gas in thermal swirled vortices with local heating of the underlying surface, taking into account the action of gravity and Coriolis forces.

Sign in / Sign up

Export Citation Format

Share Document