Large‐time behavior of solutions to the 3‐D flow of a compressible viscous micropolar fluid with cylindrical symmetry

Abstract

In this paper, we study the asymptotic behavior of global weak solutions in H1 to the problem that describes compressible viscous and heat‐conducting micropolar fluid flow in a three‐dimensional domain bounded by two circular, coaxial, and infinite cylinders that present the solid thermoinsulated walls. In the thermodynamical sense, the fluid is perfect and polytropic. We prove that the global weak solution exists and converges to a steady state as time goes to infinity. We have been working under the assumption that the initial data are cylindrically symmetric and the initial total energy is sufficiently small.

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

“…Recently, for the spherical symmetric model of described micropolar fluid in an exterior unbounded domain, we proved the large time behavior for spherically symmetric flow of viscous polytropic gas with large initial data in [26]. In the case of cylinder symmetry, which model described micropolar fluid in a bounded domain with two coxial cylinders that present the solid thermoinsulated walls, Dražić and Mujaković [11] established the local existence of generalized solutions, then they proved global existence [12] and the uniqueness [13], Huang and Dražić [21,22] studied the large time behavior of the cylindrically symmetric with small initial data, but the regularity is open. Besides, we would like to mention the work on the global wellposedness of the three-dimensional magnetohydrodynamic equations, Wang and Wang [41] obtained the global existence results for classical 3-D MHD (α = 1).…”

Research on the Mechanical Characteristics of Cyclic Loading and Unloading of Rock Based on Infrared Thermal Image Analysis

“…In continuum mechanics, if you want to start from thermodynamics, the constitutive equation must first satisfy Mathematical Problems in Engineering the Clausius-Duhamel inequality [48]. Assuming that the deformation process is infinitely small in temperature, the Clausius-Duhamel inequality can be expressed as…”

Regularity to the spherically symmetric compressible Navier–Stokes equations with density-dependent viscosity

“…For the 3-D flow of a compressible fluid with cylindrical symmetry, the global existence and the large-time behavior of generalized solutions have been proved in [1,4,5,7,15,23,26,27,32] for the isentropic and the nonisentropic cases. The corresponding study of the regularity of a solution for any given initial datum has been carried out in [17].…”