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In this work, we study the Cauchy problem of the spatially homogeneous Landauequation with hard potentials in a close-to-quilibrium framework. We prove thatthe solution to the Cauchy problem enjoys the analytic regularizing effect ofthe time variable with an L2 initial datum for positive time. So that thesmoothing effect of Cauchy problem for the spatially homogeneous Landauequation with hard potentials is exactly same as heat equation.

Analytic smoothing effect of the time variable for the spatially homogeneous Landau equation