TY - JOUR
T1 - A Remark about Time-Analyticity of the Linear Landau Equation with Soft Potential
AU - Xu , Chaojiang
AU - Xu , Yan
JO - Analysis in Theory and Applications
VL - 1
SP - 22
EP - 37
PY - 2024
DA - 2024/04
SN - 40
DO - http://doi.org/10.4208/ata.OA-2022-0029
UR - https://global-sci.org/intro/article_detail/ata/23018.html
KW - Spatially homogeneous Landau equation, analytic smoothing effect, soft potentials.
AB - <p style="text-align: justify;">In this note, we study the Cauchy problem of the linear spatially homogeneous Landau equation with soft potentials. We prove that the solution to the Cauchy
problem enjoys the analytic regularizing effect of the time variable with an $L^2$ initial
datum for positive time. So that the smoothing effect of Cauchy problem for the linear spatially homogeneous Landau equation with soft potentials is similar to the heat
equation.</p>