TY - JOUR
T1 - Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum
AU - Morimoto, Yoshinori
AU - Yang, Tong
PY - 2015/3
Y1 - 2015/3
N2 - We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.
AB - We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.
KW - Boltzmann equation
KW - Coercivity estimate
KW - Measure initial datum
KW - Smoothing effect
UR - http://www.scopus.com/inward/record.url?scp=84926124451&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84926124451&origin=recordpage
U2 - 10.1016/j.anihpc.2013.12.004
DO - 10.1016/j.anihpc.2013.12.004
M3 - RGC 21 - Publication in refereed journal
SN - 0294-1449
VL - 32
SP - 429
EP - 442
JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
IS - 2
ER -