TY - JOUR
T1 - On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials
AU - Qi, Kunlun
PY - 2021/5
Y1 - 2021/5
N2 - The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness of measure-valued solution under Grad’s angular cutoff assumption, based on which, we further obtain the existence of non-cutoff solution, for both finite and infinite energy initial datum, by a delicate compactness argument. In addition, the moments propagation and energy dissipation properties are justified for the obtained measure-valued solution as well.
AB - The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness of measure-valued solution under Grad’s angular cutoff assumption, based on which, we further obtain the existence of non-cutoff solution, for both finite and infinite energy initial datum, by a delicate compactness argument. In addition, the moments propagation and energy dissipation properties are justified for the obtained measure-valued solution as well.
KW - Boltzmann equation
KW - Measure valued solution
KW - Fourier transform
KW - Non-cutoff assumption
KW - Soft potentials
KW - Inelastic
KW - Probability measure
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85105387806&origin=recordpage
U2 - 10.1007/s10955-021-02762-w
DO - 10.1007/s10955-021-02762-w
M3 - 21_Publication in refereed journal
VL - 183
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 2
M1 - 27
ER -