Heat-conducting Micropolar Fluid Research Articles

Global Dynamics of 3D Compressible Viscous and Heat-Conducting Micropolar Fluids with Vacuum at Infinity

Global Dynamics of 3D Compressible Viscous and Heat-Conducting Micropolar Fluids with Vacuum at Infinity

Global Dynamics of 3-D Compressible Micropolar Fluids with Vacuum and Large Oscillations

This paper deals with the Cauchy problem to three-dimensional compressible viscous and heat-conducting micropolar fluid model. We establish the global existence and uniqueness of classical solution to this specific system with small initial energy. In particular, the small initial energy allows the solution to have large oscillations and initial density may contain a vacuum.

The nonstationary flows of micropolar fluids with thermal convection: An iterative approach

<p style='text-indent:20px;'>We consider a problem that describes the motion of a viscous incompressible and heat-conducting micropolar fluids in a bounded domain <inline-formula><tex-math id="M1">\begin{document}$ \Omega \subset \mathbb{R}^3 $\end{document}</tex-math></inline-formula>. We use an iterative method to analyze the existence, uniqueness, and regularity of the solutions. We also determine the convergence rates in several norms.

Exponential stability and regularity of compressible viscous micropolar fluid with cylinder symmetry

&lt;p style='text-indent:20px;'&gt;This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;$ R^3 $&lt;/tex-math&gt;&lt;/inline-formula&gt; bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a thermodynamical sense perfect and polytropic. We prove that the regularity and the exponential stability in &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;$ H^2 $&lt;/tex-math&gt;&lt;/inline-formula&gt;.&lt;/p&gt;

Global attractors for a nonlinear one-dimensional compressible viscous micropolar fluid model

This paper considers the dynamical behavior of solutions of constitutive systems for 1D compressible viscous and heat-conducting micropolar fluids. With proper constraints on initial data, we prove the existence of global attractors in generalized Sobolev spaces $$H_{\delta }^{(1)}$$ and $$H_{\delta }^{(2)}$$ . These attractors are unique in corresponding phase spaces.

Exponential stability for the compressible micropolar fluid with cylinder symmetry in R3

This paper is concerned with three-dimensional compressible viscous and heat-conducting micropolar fluid in the domain to the subset of R3 bounded with two coaxial cylinders that present the solid thermoinsulated walls, being in a perfect and polytropic thermodynamical sense. We prove that cylindrically symmetric solutions decay to a constant exponentially as time goes to infinity based on the assumptions that the initial total energy is sufficiently small and initial data are sufficiently smooth cylindrically symmetric functions.

Global classical large solution to compressible viscous micropolar and heat-conducting fluids with vacuum

In this paper we consider the non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. Since the strong nonlinearity and degeneracies of the equations due to the temperature equation and vanishing of density, there are a few results about global existence of classical solution to this model. In the paper, we obtain a global classical solution to the equations with large initial data and vacuum. Moreover, we get the uniqueness of the solution to this system without vacuum. The analysis is based on the assumption \begin{document}$ \kappa(\theta) = O(1+\theta^q) $\end{document} where \begin{document}$ q\geq0 $\end{document} and delicate energy estimates.

3-D flow of a compressible viscous micropolar fluid model with spherical symmetry: A brief survey and recent progress

We consider the non-stationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid with the assumption of spherical symmetry. We analyze the flow between two concentric spheres that present solid thermo-insulated walls. The fluid is perfect and polytropic in the thermodynamical sense and the initial density and temperature are strictly positive. The corresponding problem has homogeneous boundary data. In this work, we present the described model and provide a brief overview of the progress in the mathematical analysis of the associated initial-boundary problem. We consider existence and uniqueness of the generalized solution, asymptotic behavior of the solution and regularity of the solution.

Three-dimensional compressible viscous micropolar fluid with cylindrical symmetry: Derivation of the model and a numerical solution

In this paper we consider the nonstationary 3D flow of a compressible viscous and heat-conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic. The fluid domain is the subset of R3 bounded with two coaxial cylinders that present solid thermoinsulated walls. We assume that the initial mass density, temperature, as well as the velocity and microrotation vectors are radially dependent only. The corresponding solution is also spatially radially dependent. We derive the mathematical model in the Lagrangian description and by using the Faedo–Galerkin method we introduce a system of approximate equations and construct its solutions. We also analyze two numerical examples.

Global solution to 3D problem of a compressible viscous micropolar fluid with spherical symmetry and a free boundary

We consider a nonstationary 3D flow of a compressible viscous heat-conducting micropolar fluid, which is in the thermodynamical sense perfect and polytropic, in the domain bounded with two concentric spheres in R3. In this paper we establish the existence of a global solution to the free boundary problem defined with the homogeneous boundary conditions for velocity, microrotation, heat flux on the fixed border and homogeneous boundary conditions for strain, microrotation, and heat flux on the free boundary. We suppose that the initial data are spherically symmetric, with positive initial density and temperature, having the zero density on the free boundary. Because of the spherical symmetry, the starting three-dimensional problem is transformed to the one-dimensional problem in Lagrangian coordinates in the domain that is a segment. The solution to our problem is obtained as a limit of the sequence of approximate solutions derived from suitable semi-discrete finite difference approximate systems. By using the derived bounded estimates of the approximate solutions and the results of the weak and strong compactness, we establish the convergence to the generalized solution of our problem globally in time.

Global solution to 1D model of a compressible viscous micropolar heat-conducting fluid with a free boundary

In this paper we consider the nonstationary 1D flow of the compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamically sense perfect and polytropic. The fluid is between a static solid wall and a free boundary connected to a vacuum state. We take the homogeneous boundary conditions for velocity, microrotation and heat flux on the solid border and that the normal stress, heat flux and microrotation are equal to zero on the free boundary. The proof of the global existence of the solution is based on a limit procedure. We define the finite difference approximate equations system and construct the sequence of approximate solutions that converges to the solution of our problem globally in time.

3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Regularity of the solution

In this paper we consider the nonstationary 3-D flow of a compressible viscous and heat-conducting micropolar fluid, that is in the thermodynamical sense perfect and polytropic. The fluid domain is a subset of R3 bounded with two concentric spheres that present the solid thermoinsulated walls. The corresponding mathematical model is set up in the Lagrangian description. We assume that the initial data are spherically symmetric functions, and that the initial density and temperature are strictly positive. This problem has a unique spherically symmetric generalized solution globally in time. Here we introduce the Hölder continuous initial functions and prove that, for any T>0, the state function is also Hölder continuous.

3-D flow of a compressible viscous micropolar fluid with spherical symmetry: a global existence theorem

We consider the nonstationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain to be the subset of \(\mathbf{R}^{3}\) bounded with two concentric spheres that present the solid thermo-insulated walls. In the thermodynamical sense the fluid is perfect and polytropic. We assume that the initial density and temperature are bounded from below with a positive constant and that the initial data are sufficiently smooth spherically symmetric functions. The starting problem is transformed into the Lagrangian description on the spatial domain \(]0,1[\). In this work we prove that our problem has a generalized solution for any time interval \([0,T ]\), \(T\in\mathbf{R}^{+}\). The proof is based on the local existence theorem and the extension principle.

3-D flow of a compressible viscous micropolar fluid with spherical symmetry: Large time behavior of the solution

We consider the non-stationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain that is the subset of R3 bounded with two concentric spheres that present solid thermo-insulated walls. Under the assumption that the fluid is perfect and polytropic in the thermodynamical sense as well as that the initial density and temperature are strictly positive and that the initial data are sufficiently smooth spherically symmetric functions, the corresponding problem with homogeneous boundary data has a unique generalized solution for any time interval [0,T], T∈R+. In this work we analyze large time behavior of the solution and prove its stabilization.

3-D flow of a compressible viscous micropolar fluid with spherical symmetry: uniqueness of a generalized solution

We consider nonstationary 3-D flow of a compressible viscous heat-conducting micropolar fluid in the domain that is the subset of bounded with two concentric spheres that present the solid thermoinsulated walls. In the thermodynamical sense the fluid is perfect and polytropic. If we assume that the initial density and temperature are strictly positive and that the initial data are sufficiently smooth spherically symmetric functions then our problem has a generalized solution for a sufficiently small time interval. We study the problem in the Lagrangian description and prove the uniqueness of its generalized solution.

The existence of a global solution for one dimensional compressible viscous micropolar fluid with non-homogeneous boundary conditions for temperature

We consider non-stationary 1-D flow of a compressible viscous heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity and microrotation, as well as non-homogeneous boundary conditions for temperature are introduced. This problem has a unique generalized solution locally in time. With the help of this result and using the principle of extension we prove a global-in-time existence theorem.

1-D compressible viscous micropolar fluid model with non-homogeneous boundary conditions for temperature: A local existence theorem

We consider non-stationary 1-D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in thermodynamical sense perfect and polytropic. The homogeneous boundary conditions for velocity and microrotation, as well as non-homogeneous boundary conditions for temperature are assumed. Using the Faedo–Galerkin method we prove a local-in-time existence of a generalized solution.

One-Dimensional Compressible Viscous Micropolar Fluid Model: Stabilization of the Solution for the Cauchy Problem

We consider the Cauchy problem for nonstationary 1D flow of a compressible viscous and heat-conducting micropolar fluid, assuming that it is in the thermodynamical sense perfect and polytropic. This problem has a unique generalized solution on for each . Supposing that the initial functions are small perturbations of the constants we derive a priori estimates for the solution independent of , which we use in proving of the stabilization of the solution.

Nonhomogeneous Boundary Value Problem for One-Dimensional Compressible Viscous Micropolar Fluid Model: Regularity of the Solution

An initial-boundary value problem for 1D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is thermodynamically perfect and polytropic. Assuming that the initial data are Holder continuous on and transforming the original problem into homogeneous one, we prove that the state function is Holder continuous on , for each . The proof is based on a global-in-time existence theorem obtained in the previous research paper and on a theory of parabolic equations.

Non-homogeneous boundary value problem for one-dimensional compressible viscous micropolar fluid model: a local existence theorem

An initial-boundary value problem for 1-D flow of a compressible viscous heat-conducting micropolar fluid is considered; the fluid is assumed thermodynamically perfect and polytropic. The original problem is transformed into homogeneous one and studied the Faedo-Galerkin method. A local-in-time existence of generalized solution is proved.