TY - JOUR
T1 - Local existence with mild regularity for the Boltzmann equation
AU - Alexandre, Radjesvarane
AU - Morimoto, Yoshinori
AU - Ukai, Seiji
AU - Xu, Chao-Jiang
AU - Yang, Tong
PY - 2013/12
Y1 - 2013/12
N2 - Without Grad's angular cutoff assumption, the local existence of classical solutions to the Boltzmann equation is studied. There are two new improvements: the index of Sobolev spaces for the solution is related to the parameter of the angular singularity; moreover, we do not assume that the initial data is close to a global equilibrium. Using the energy method, one important step in the analysis is the study of fractional derivatives of the collision operator and related commutators © American Institute of Mathematical Sciences.
AB - Without Grad's angular cutoff assumption, the local existence of classical solutions to the Boltzmann equation is studied. There are two new improvements: the index of Sobolev spaces for the solution is related to the parameter of the angular singularity; moreover, we do not assume that the initial data is close to a global equilibrium. Using the energy method, one important step in the analysis is the study of fractional derivatives of the collision operator and related commutators © American Institute of Mathematical Sciences.
KW - Boltzmann equation
KW - Energy estimates
KW - Existence of solution
KW - Fractional derivatives
UR - http://www.scopus.com/inward/record.url?scp=84888404493&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84888404493&origin=recordpage
U2 - 10.3934/krm.2013.6.1011
DO - 10.3934/krm.2013.6.1011
M3 - RGC 21 - Publication in refereed journal
SN - 1937-5093
VL - 6
SP - 1011
EP - 1041
JO - Kinetic and Related Models
JF - Kinetic and Related Models
IS - 4
ER -