1203.0130 (Nicolas Fournier)

Finiteness of entropy for the homogeneous Boltzmann equation with
measure initial condition    [PDF]

Nicolas Fournier

We consider the 3D spatially homogeneous Boltzmann equation for (true) hard and moderately soft potentials. We assume that the initial condition is a probability measure with finite energy and is not a Dirac mass. For hard potentials, we prove that any reasonable weak solution immediately belongs to some Besov space. For moderately soft potentials, we assume additionally that the initial condition has a moment of sufficiently high order (8 is enough) and prove the existence of a solution that immediately belongs to some Besov space. The considered solutions thus instantaneously become functions with a finite entropy. We also prove that in any case, any weak solution is immediately supported by $\rr^3$.

View original: http://arxiv.org/abs/1203.0130