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Kinetic theory of spatially homogeneous systems with long-range interactions: I. General results
Pierre-Henri Chavanis
We review and complete the existing literature on the kinetic theory of spatially homogeneous systems with long-range interactions taking collective effects into account. The evolu…
Kinetic theory of Onsager's vortices in two-dimensional hydrodynamics
Pierre-Henri Chavanis
Starting from the Liouville equation, and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body…
Kinetic theory of two-dimensional point vortices with collective effects
Pierre-Henri Chavanis
We develop a kinetic theory of point vortices in two-dimensional hydrodynamics taking collective effects into account. We first recall the approach of Dubin & O'Neil [Phys. Rev. Le…
Kinetic theory of long-range interacting systems with angle-action variables and collective effects
Pierre-Henri Chavanis
We develop a kinetic theory of systems with long-range interactions taking collective effects and spatial inhomogeneity into account. Starting from the Klimontovich equation and us…
Instability of a uniformly collapsing cloud of classical and quantum self-gravitating Brownian particles
Pierre-Henri Chavanis
We study the growth of perturbations in a uniformly collapsing cloud of self-gravitating Brownian particles. This problem shares analogies with the formation of large-scale structu…