Gelfand-Shilov Smoothing Effect for the Radially Symmetric Spatially Homogeneous Landau Equation under the Hard Potential $\gamma=2$

Abstract

Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potential $\gamma=2$ in perturbation framework, we prove the existence and Gelfand-Shilov smoothing effect for solution to the Cauchy problem of the symmetric homogenous Landau equation with small initial datum.