TY - JOUR
T1 - Time-Velocity Decay of Solutions to the Non-Cutoff Boltzmann Equation in the Whole Space
AU - Cao , Chuqi
AU - Duan , Renjun
AU - Li , Zongguang
JO - Communications in Mathematical Analysis and Applications
VL - 1
SP - 61
EP - 120
PY - 2024
DA - 2024/03
SN - 3
DO - http://doi.org/10.4208/cmaa.2024-0003
UR - https://global-sci.org/intro/article_detail/cmaa/22940.html
KW - Boltzmann equation, angular non-cutoff, large time behavior.
AB - <p style="text-align: justify;">In this paper, we consider the perturbed solutions with polynomial
tail in large velocities for the non-cutoff Boltzmann equation near global Maxwellians in the whole space. The global in time existence is proved in the
weighted Sobolev spaces and the almost optimal time decay is obtained in
Fourier transform based low-regularity spaces. The result shows a time-velocity decay structure of solutions that can be decomposed into two parts. One
part allows the slow polynomial tail in large velocities, carries the initial data
and enjoys the exponential or arbitrarily large polynomial time decay. The
other part, with zero initial data, is dominated by the non-negative definite
symmetric dissipation and has the exponential velocity decay but only the slow
polynomial time decay.</p>