The Boltzmann equation for plane Couette flow in a finite channel. (English) Zbl 07835877
The paper studies the Boltzmann equation for hard potentials with angular cutoff in the channel domain \(\mathbb{T}\times[-1,1]\times \mathbb{T}\) with isothermal and moving boundaries at \(x_2=-1\) and \(x_2=1\), respectively. On the boundaries \(x_2=\pm 1\), the authors consider the diffuse reflection boundary conditions. R.-J. Duan et al. [“The Boltzmann equation for plane Couette flow”, Preprint, arXiv:2107.02458] recently proved the existence of a unique steady solution to this boundary value problem, and the authors of this paper prove the local stability of the steady state. The authors also prove that there is a unique global solution which converges to the steady state exponentially fastly in the weighted \(L^\infty\) norm.
Reviewer: Jin Woo Jang (Pohang)
Keywords:
solution existence; uniqueness; local dynamical stability; angular cutoff hard potential; asymptotic convergence to steady state; exponential time decay rateReferences:
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