Global solutions for a one-dimensional compressible micropolar fluid model with zero heat conductivity

Abstract

In this study, we consider global solutions for the one-dimensional compressible micropolar fluid model with zero heat conductivity, which is a hyperbolic–parabolic system. The pressure, velocity, and angular velocity are dissipative because of the viscosity, whereas the entropy is non-dissipative due to the absence of heat conductivity. Compared with the classical Navier–Stokes equations, there is an extra angular velocity ω in the micropolar fluid model, which causes both benefits and problems. The benefit is due to the fact that the term −vω is a damping term and it provides extra regularity for ω, and the problem is due to the term vω2 because it increases the nonlinearity of the system. The global solutions can be obtained by combining the local existence and a priori estimates if the H2-norm of the initial perturbation around a constant state is sufficiently small. The asymptotic behavior is also determined in this study.