TY - JOUR
T1 - Exterior problem for the Boltzmann equation with temperature difference
T2 - asymptotic stability of steady solutions
AU - Jia, Xuanji
PY - 2017/3/15
Y1 - 2017/3/15
N2 - The asymptotic stability of non-equilibrium steady solutions to the exterior problem for the Boltzmann equation was first proved by Ukai and Asano in [17], under the assumption that the temperature associating with the far-field Maxwellian and the one preserved by the kinetic boundary condition are the same. In this paper, we generalize Ukai and Asano's result in the sense that the two temperatures mentioned above are allowed to be different. The proof of the main theorem is based on the ideas developed in [16,17] and [20] as well as some new observations.
AB - The asymptotic stability of non-equilibrium steady solutions to the exterior problem for the Boltzmann equation was first proved by Ukai and Asano in [17], under the assumption that the temperature associating with the far-field Maxwellian and the one preserved by the kinetic boundary condition are the same. In this paper, we generalize Ukai and Asano's result in the sense that the two temperatures mentioned above are allowed to be different. The proof of the main theorem is based on the ideas developed in [16,17] and [20] as well as some new observations.
KW - Asymptotic stability
KW - Boltzmann equation
KW - Exterior problem
KW - Steady solutions
KW - Temperature difference
UR - http://www.scopus.com/inward/record.url?scp=85007560424&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85007560424&origin=recordpage
U2 - 10.1016/j.jde.2016.11.039
DO - 10.1016/j.jde.2016.11.039
M3 - 21_Publication in refereed journal
VL - 262
SP - 3642
EP - 3688
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 6
ER -