Global attractor for a nonlinear one-dimensional compressible viscous micropolar fluid

TL;DR

This paper investigates the long-term behavior of solutions to a 1D compressible viscous micropolar fluid model, proving the existence of global attractors in specific Sobolev spaces under certain initial conditions.

Contribution

It establishes the existence of global attractors for the 1D compressible viscous micropolar fluid equations in generalized Sobolev spaces, which was not previously known.

Findings

Existence of global attractors in $H^{(1)}_{eta}$ and $H^{(2)}_{eta}$ spaces.

Conditions on initial data for attractor existence.

Mathematical framework for long-term dynamics of micropolar fluids.

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 $H^{(1)}_{\delta}$ and $H^{(2)}_{\delta}$.