On Smooth Solutions to the Thermostated Boltzmann Equation with Deformation Article Swipe

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Boltzmann equation Steady state (chemistry) Boltzmann constant Classical mechanics Torus Mathematical analysis Physics Homogeneous Deformation (meteorology) Collision Mathematics Statistical physics Thermodynamics Geometry Chemistry Computer science Physical chemistry Meteorology Computer security

Renjun Duan , Shuangqian Liu ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.4208/cmaa.2021-0004 · OA: W4205444132

This paper concerns a kinetic model of the thermostated Boltzmann equation with a linear deformation force described by a constant matrix. The collision kernel under consideration includes both the Maxwell molecule and general hard potentials with angular cutoff. We construct the smooth steady solutions via a perturbation approach when the deformation strength is sufficiently small. The steady solution is a spatially homogeneous non Maxwellian state and may have the polynomial tail at large velocities. Moreover, we also establish the long time asymptotics toward steady states for the Cauchy problem on the corresponding spatially inhomogeneous equation in torus, which in turn gives the non-negativity of steady solutions.