Gelfand-Shilov Smoothing Effect for the Radially Symmetric SpatiallyHomogeneous Landau Equation under the Hard Potentialγ=2

Based on the spectral decomposition for the linear and nonlinear radially symmetric homogeneous non-cutoff Landau operators under the hard potentialγ=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.