Global behavior for the classical solution of compressible viscous micropolar fluid with cylinder symmetry

Abstract

<p style='text-indent:20px;'>This paper is concerned with the global solutions of the 3D compressible micropolar fluid model in the domain to a subset of <inline-formula><tex-math id="M1">\begin{document}$ R^3 $\end{document}</tex-math></inline-formula> bounded with two coaxial cylinders that present the solid thermo-insulated walls, which is in a thermodynamical sense perfect and polytropic. Compared with the classical Navier-Stokes equations, the angular velocity <inline-formula><tex-math id="M2">\begin{document}$ w $\end{document}</tex-math></inline-formula> in this model brings benefit that is the damping term -<inline-formula><tex-math id="M3">\begin{document}$ uw $\end{document}</tex-math></inline-formula> can provide extra regularity of <inline-formula><tex-math id="M4">\begin{document}$ w $\end{document}</tex-math></inline-formula>. At the same time, the term <inline-formula><tex-math id="M5">\begin{document}$ uw^2 $\end{document}</tex-math></inline-formula> is bad, it increases the nonlinearity of our system. Moreover, the regularity and exponential stability in <inline-formula><tex-math id="M6">\begin{document}$ H^4 $\end{document}</tex-math></inline-formula> also are proved.</p>

Large-time behavior of solutions to the compressible micropolar fluid with shear viscosity

“…The technique to prove Remark 1.3 is similar with the references [45,27], where, the main idea can be also found in literatures [38,40].…”

“…For recent progress in the mathematical analysis of this model, we refer to [7,12,18,22,24,26]. For the cylindrically symmetric model of the described micropolar fluid in a bounded annular domain, the local existence of generalized solutions [11], the uniqueness and global existence [19], and the large-time behavior and exponential stability of solutions [20,21,45,27] were established under certain assumptions on the initial energy. In this paper, assumptions for the model are that the flow is isotropic, viscous, and heat-conducting, as well as that the fluid is perfect and polytropic in the thermodynamical sense.…”

Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method

“…One of the most important of these conditions is the symmetry condition, whose importance lies in the fact that in 1D, 2D, and 3D problems it enables the study medium to be reduced and, thus, shortens the simulation time. Its applicability stands out in numerous engineering problems where there is symmetry, such as in cylindrical or square columns, either for the study of heat transmission, chloride diffusion, etc., or its application to different types of storage tanks where several phenomena can be studied [34][35][36].…”