TY - JOUR
T1 - Smoothing Estimates for Boltzmann Equation with Full-range Interactions
T2 - Spatially Inhomogeneous Case
AU - Chen, Yemin
AU - He, Lingbing
PY - 2012/2
Y1 - 2012/2
N2 - In this paper, we study the regularity of the solution to the Boltzmann equation with full-range interactions but for the spatially inhomogeneous case. Under the initial regularity assumption on the solution itself, we show that the solution will become immediately smooth for all the variables as long as the time is far way from zero. Our strategy relies upon the new upper and lower bounds for the collision operator established in Chen and He (Arch Ration Mech Anal 201(2):501-548, 2011), a hypo-elliptic estimate for the transport equation and the element energy method.
AB - In this paper, we study the regularity of the solution to the Boltzmann equation with full-range interactions but for the spatially inhomogeneous case. Under the initial regularity assumption on the solution itself, we show that the solution will become immediately smooth for all the variables as long as the time is far way from zero. Our strategy relies upon the new upper and lower bounds for the collision operator established in Chen and He (Arch Ration Mech Anal 201(2):501-548, 2011), a hypo-elliptic estimate for the transport equation and the element energy method.
UR - http://www.scopus.com/inward/record.url?scp=84863079032&partnerID=8YFLogxK
U2 - 10.1007/s00205-011-0482-3
DO - 10.1007/s00205-011-0482-3
M3 - Article
AN - SCOPUS:84863079032
SN - 0003-9527
VL - 203
SP - 343
EP - 377
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -