Global strong solution for initial–boundary value problem of one-dimensional compressible micropolar fluids with density dependent viscosity and temperature dependent heat conductivity

2018 ◽  
Vol 42 ◽  
pp. 71-92 ◽  
Author(s):  
Ran Duan
Keyword(s):  
Boundary Value Problem ◽  
Heat Conductivity ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Temperature Dependent ◽  
Micropolar Fluids ◽  
One Dimensional ◽  
Global Strong Solution ◽  
Initial Boundary Value ◽  
Dependent Viscosity

scholarly journals An Initial Boundary Value Problem for the Zakharov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Quankang Yang ◽  
Charles Bu
Keyword(s):  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Zakharov Equation ◽  
One Dimensional ◽  
Global Strong Solution ◽  
The One ◽  
Initial Boundary Value

This paper studies an inhomogeneous initial boundary value problem for the one-dimensional Zakharov equation. Existence and uniqueness of the global strong solution are proved by Galerkin’s method and integral estimates.

A NONLINEAR PARABOLIC SYSTEM ARISING IN THERMOMECHANICS AND IN THERMOMAGNETISM

1992 ◽  
Vol 02 (03) ◽  
pp. 271-281 ◽  
Author(s):  
JOSÉ-FRANCISCO RODRIGUES
Keyword(s):  
Parabolic Equations ◽  
Eddy Currents ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Arbitrary Cross Section ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Nonlinear Parabolic ◽  
Initial Boundary Value ◽  
Dependent Viscosity

We consider a system of two parabolic equations modeling the thermo-convection of a Newtonian fluid, with temperature dependent viscosity of energy dissipation, as well as the thermal effects of the eddy currents, induced by a slowly varying magnetic field, in cylinders with arbitrary cross-section. We show the existence of a weak solution of the corresponding initial-boundary value problem and, under additional assumptions, we consider the question of the uniqueness and regularity of the solution.

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

scholarly journals Global strong solution to the 2D inhomogeneous incompressible magnetohydrodynamic fluids with density-dependent viscosity and vacuum

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Menglong Su
Keyword(s):  
Strong Solution ◽  
Blow Up ◽  
Strong Solutions ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Density Dependent ◽  
Global Strong Solution ◽  
Mhd System ◽  
Initial Boundary Value ◽  
Dependent Viscosity

AbstractIn this paper, we investigate an initial boundary value problem for two-dimensional inhomogeneous incompressible MHD system with density-dependent viscosity. First, we establish a blow-up criterion for strong solutions with vacuum. Precisely, the strong solution exists globally if $\|\nabla \mu (\rho )\|_{L^{\infty }(0, T; L^{p})}$ ∥ ∇ μ ( ρ ) ∥ L ∞ ( 0 , T ; L p ) is bounded. Second, we prove the strong solution exists globally (in time) only if $\|\nabla \mu (\rho _{0})\|_{L^{p}}$ ∥ ∇ μ ( ρ 0 ) ∥ L p is suitably small, even the presence of vacuum is permitted.

Weak solutions to the initial-boundary value problem for the shearing of non-homogeneous thermoviscoplastic materials

1989 ◽  
Vol 113 (3-4) ◽  
pp. 257-265 ◽  
Author(s):  
Nicolas Charalambakis ◽  
François Murat
Keyword(s):  
Weak Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Weak Solutions ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Temperature Dependent ◽  
Initial Boundary Value

SynopsisWe prove the existence of a weak solution for the system of partial differential equations describing the shearing of stratified thermoviscoplastic materials with temperature-dependent non-homogeneous viscosity.

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