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arXiv · 2004.09300

Hypoelliptic and spectral estimates for the linearized Landau operator

Mohamad Rachid
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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 $\ge$ 0, the density of particles at position x $\in$ R 3 and velocity v $\in$ 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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Mohamad Rachid. 2020-04-17. Hypoelliptic and spectral estimates for the linearized Landau operator. https://doi.org/10.2140/paa.2023.5.1

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