Gelfand–Shilov smoothing effect of the spatially homogeneous Landau equation with moderately soft potential

Abstract

In this work, we study the nonlinear spatially homogeneous Landau equation with moderately soft potential in a close‐to‐equilibrium framework, we show that the solution to the Cauchy problem with initial datum enjoys a Gelfand–Shilov regularizing effect, meaning that the solution of the Cauchy problem and its Fourier transformation are Gevery smoothness for any positive time.