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

Abstract

Abstract. 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. By transforming the original problem into homogeneous one we prove a global-in-time existence theorem. The proof is based on a local existence theorem, obtained in the previous research paper [5].Mathematics subject classification (2000): 35K55, 35Q40, 76N10, 46E35.

Global Existence and Uniqueness of Nonlinear Evolutionary Fluid Equations

“…Qin [99] has flexibly modified Okada's subtle method and obtained a series of properties concerning global existence, regularity, exponential stability and existence of attractors. Recently, in the case of micropolar fluids, Mujaković has extended the study to case of non-homogeneous boundary value problems (see, e.g., [85]). Earlier also in [84] and [79], she derived similar results, including results on the large-time behavior of solutions.…”

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

“…(1) Under suitably prescribed initial data for 1D micropolar fluid model, N. Mujavokić [24] established the global existence and asymptotic behavior of the solution for the system (1.1) with the boundary conditions (1.2) in [25,26], then the authors obtained the exponential stability in [17,27,28] and established the local existence and global existence for the same system with non-homogeneous boundary conditions for velocity and microrotation:…”

Asymptotic stability of a composite wave for the one-dimensional compressible micropolar fluid model without viscosity

“…The mathematical theory of the compressible micropolar fluid model has been studied extensively in the last several decades. For the non-isentropic case, Mujaković first analyzed the one-dimensional model and obtained a series of results concerning the local-in-time existence and uniqueness, the global existence and regularity of solutions to an initial-boundary value problem with homogeneous [4,5,6] and non-homogeneous [7,8,9] boundary conditions. Besides, she also studied the large time behavior of the solutions to initial-boundary value problem [10] and the Cauchy problem [11] of the one-dimensional model.…”