Landau damping in finite regularity for unconfined systems with screened interactions

2016/04/20 by Bedrossian, Jacob, Masmoudi, Nader, Mouhot, Clement · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Plasma Physics (physics.plasm-ph)

paper · doi:10.48550/arxiv.1604.05783

Abstract

We prove Landau damping for the collisionless Vlasov equation with a class of L¹ interaction potentials (including the physical case of screened Coulomb interactions) on \mathbb R³_x × \mathbb R³_v for localized disturbances of an infinite, homogeneous background. Unlike the confined case \mathbb T³_x × \mathbb R_v³, results are obtained for initial data in Sobolev spaces (as well as Gevrey and analytic classes). For spatial frequencies bounded away from zero, the Landau damping of the density is similar to the confined case. The finite regularity is possible due to an additional dispersive mechanism available on \mathbb R_x³ which reduces the strength of the plasma echo resonance.

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