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Hypoelliptic and spectral estimates for the linearized Landau operator

Abstract

We are interested in the inhomogeneous Landau equation which describes the evolution of a particle density f = f (t, x, v) representing at time t ≥ 0, the density of particles at position x ∈ R 3 and velocity v ∈ R 3. The study is motivated by the linearization of the Landau equation near Maxwellian distribution. In this article, we establish hypoelliptic estimates, a localization of the spectrum and estimates of the resolvent of the linear Landau operator with hard potentials and Maxwellian molecules. The proof is based on a multiplier method and requires fine pseudo-differential calculus tools.
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Dates and versions

hal-02545717 , version 1 (17-04-2020)
hal-02545717 , version 2 (07-12-2020)

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Mohamad Rachid. Hypoelliptic and spectral estimates for the linearized Landau operator. 2020. ⟨hal-02545717v2⟩
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