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Cauchy Problem for the Spatially Homogeneous Landau Equation with Shubin Class Initial Datum and Gelfand--Shilov Smoothing Effect
In this work, we study the nonlinear spatially homogeneous Landau equation with Maxwellian molecules; by using the spectral analysis, we show that the nonlinear Landau operator is almost linear, and we prove the existence of a weak solution for the Cauchy problem with the initial datum belonging to the Shubin …