TY - JOUR
T1 - Regularity of solutions to the spatially homogeneous Boltzmann equation for non Maxwellian molecules without angular cutoff
AU - Lin, Shiyou
PY - 2009/7/1
Y1 - 2009/7/1
N2 - In this paper, we use the pseudo-differential calculus to analyze the smoothing property of weak solutions to the spatially homogeneous Boltzmann equation. Precisely, we show that for the non-Maxwellian molecules with Debye-Yukawa potential, if the positive weak solution is Lipschitz continuous in the velocity variable, then it lies in the Sobolev space Hloc+∞(R3) and hence it is automatically smooth.
AB - In this paper, we use the pseudo-differential calculus to analyze the smoothing property of weak solutions to the spatially homogeneous Boltzmann equation. Precisely, we show that for the non-Maxwellian molecules with Debye-Yukawa potential, if the positive weak solution is Lipschitz continuous in the velocity variable, then it lies in the Sobolev space Hloc+∞(R3) and hence it is automatically smooth.
KW - Boltzmann equation
KW - Debye-Yukawa potential
KW - Non-cutoff
KW - Regularity
KW - Pseudo-differential operators
UR - http://www.scopus.com/inward/record.url?scp=64849105795&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-64849105795&origin=recordpage
U2 - 10.1016/j.na.2008.10.099
DO - 10.1016/j.na.2008.10.099
M3 - RGC 21 - Publication in refereed journal
SN - 0362-546X
VL - 71
SP - 666
EP - 673
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 1-2
ER -