@Article{CMAA-1-1,
author = {Renjun, Duan and Shuangqian, Liu},
title = {On Smooth Solutions to the Thermostated Boltzmann Equation with Deformation},
journal = {Communications in Mathematical Analysis and Applications},
year = {2022},
volume = {1},
number = {1},
pages = {152--212},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2790-1939},
doi = {https://doi.org/10.4208/cmaa.2021-0004},
url = {https://global-sci.com/article/81427/on-smooth-solutions-to-the-thermostated-boltzmann-equation-with-deformation}
}