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 (Formula presented.) for localized disturbances of an infinite, homogeneous background. Unlike the confined case (Formula presented.), results are obtained for initial data in Sobolev spaces (as well as Gevrey and analytic classes). For spatial frequencies bounded away from 0, 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 (Formula presented.) that reduces the strength of the plasma echo resonance.
ASJC Scopus subject areas
- Applied Mathematics