Hypoelliptic and spectral estimates for the linearized Landau operator

Mohamad Rachid (1, 2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 UN UFR ST - Université de Nantes - UFR des Sciences et des Techniques

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.

Domaines: Equations aux dérivées partielles [math.AP]; Théorie spectrale [math.SP]; Analyse fonctionnelle [math.FA]

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