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We study the Landau equation for a mixture of two species in the whole space,with initial condition of one species near a vacuum and the other near aMaxwellian equilibrium state. For the linearized level, without any smoothnessassumption on the initial data, it is shown that the solution becomes smoothinstantaneously in both the space and momentum variables. Moreover, the largetime behavior of the solution is also obtained.

Smoothing effects and decay estimate of the solution of the linearized two species Landau equation