The Boltzmann equation for plane Couette flow in a finite channel

The dynamics of a rarefied gas in a finite channel with the same temperatures and opposite velocities is a fundamental problem in kinetic theory. The relative motion of the planar boundaries can induce a non-equilibrium state which is referred to as the Couette flow. In this paper, we demonstrate that the unsteady Couette flow for the Boltzmann equation in 3D finite channel time asymptotically converges to the 1D steady state constructed in Duan et al. (2022), we also prove the exponential time decay rate as a byproduct. The validity of the analysis is established for all hard potentials.

Automated summary

In this paper, the dynamics of a rarefied gas in a finite channel is studied, specifically focusing on the phenomenon of Couette flow. The authors demonstrate that the unsteady Couette flow for the Boltzmann equation converges to a 1D steady state and derive the exponential time decay rate. The analysis holds for all hard potentials.