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

Abstract

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 (1) δ and H (2) δ .

Global dynamics of solutions for a sixth-order parabolic equation describing continuum evolution of film-free surface

“…The dynamic properties of diffusion systems such as the global asymptotical behaviors of solutions and global attractors are important for the study of diffusion models, which ensure the stability of diffusion phenomena and provide the mathematical foundation for the study of diffusion dynamics. For the higher-order diffusion equation, there are many classical results related to its global attractors, see, for example, Dlotko [3], Li and Zhong [7], Schimperna [10], Alouini [1], Cheskidov and Dai [2], Huang, Yang, Lu and Wang [6], Duan and Xu [4] and so on. To the best of our knowledge, the existence of the global attractor for problem (1)-(3) has not been addressed yet, which is the main goal of this article.…”

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

“…For the one-dimensional case, the compressible micropolar ideal gas model was first described by Mujaković (see [31]), and then the local existence, global existence, regularity, large time behavior, stity of the solution, and the existence of global attractors for the nonisentropic compressible micropolar ideal gas model were established in [6,13,25,28,32,33,34,35,36,37,42]. Recently, there have been several investigations on the global existence, uniqueness, regularity, and large time behavior of solutions to problems associated with the compressible micropolar real gas model in [8,2,3,4,23].…”

Stability and dynamics for a nonlinear one-dimensional full compressible non-Newtonian fluids

“…These constraints give rise to some of the major technical difficulties we have to overcome. Inspired by [12], [30], we introduce spaces:…”