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We establish a priori upper bounds for solutions to the spatiallyinhomogeneous Landau equation in the case of moderately soft potentials, witharbitrary initial data, under the assumption that mass, energy and entropydensities stay under control. Our pointwise estimates decay polynomially in thevelocity variable. We also show that if the initial data satisfies a Gaussianupper bound, this bound is propagated for all positive times.

Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials