Uniqueness of Bounded Solutions for the Homogeneous Landau Equation with a Coulomb Potential

f0(v) log f0(v)dv for all t ≥ 0. Assume that in a dilute gas or plasma, particles collide by pairs, due to a repulsive force proportional to 1/r, where r stands for the distance between the two particles. Then if s ∈ (2,∞), the velocity distribution solves the corresponding Boltzmann equation [14, 15]. But if s = 2, the Boltzmann equation is meaningless [14] and is often replaced by the Landau equation (1). However, there are also many mathematical works on the Landau equation where |z| is replaced by |z| in (2), with γ = (s − 5)/(s− 1) ∈ [−3, 1). One usually speaks of hard potentials when γ ∈ (0, 1) (i.e. s > 5), Maxwell molecules when γ = 0 (i.e. s = 5), soft potentials when γ ∈ (−3, 0) (i.e. s ∈ (2, 5)), Coulomb potential when γ = −3 (i.e. s = 2). When γ > −3, the Landau equation can be seen as an approximation of the corresponding Boltzmann equation in the asymptotic of grazing collisions [14]. This can help to understand the effect of grazing collisions in the Boltzmann equation without cutoff and is also of interest