TY - JOUR
T1 - Analytic Smoothing Effect of the Time Variable for the Spatially Homogeneous Landau Equation
AU - Xu , Chaojiang
AU - Xu , Yan
JO - Journal of Partial Differential Equations
VL - 1
SP - 88
EP - 103
PY - 2024
DA - 2024/02
SN - 37
DO - http://doi.org/10.4208/jpde.v37.n1.5
UR - https://global-sci.org/intro/article_detail/jpde/22907.html
KW - Spatially homogeneous Landau equation, analytic smoothing effect, hard potentials.
AB - <p style="text-align: justify;">In this work, we study the Cauchy problem of the spatially homogeneous
Landau equation with hard potentials in a close-to-equilibrium framework. 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 the Cauchy problem for the spatially homogeneous Landau equation with hard
potentials is exactly same as heat equation.</p>