On the spatially homogeneous Boltzmann equation

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique t...

The Spatially Homogeneous Relativistic Boltzmann Equation with a Hard Potential

In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global existence theorems. We show that global solutions exist for a certain class of collision cross sections of the hard potential type in Minkowski space and in ...

Information Geometry Formalism for the Spatially Homogeneous Boltzmann Equation

Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a suitable set E of mutually absolutely continuous densities. We study in particular the fine properties of the Kullback-Liebler divergence in this context. We also ...

About L P Estimates for the Spatially Homogeneous Boltzmann Equation

For the homogeneous Boltzmann equation with (cutoo or non cutoo) hard potentials, we prove estimates of propagation of L p norms with a weight (1+jxj 2) q=2 (1 < p < +1, q 2 R large enough), as well as appearance of such weights. The proof is based on some new functional inequalities for the collision operator, proven by elementary means.

On the Grazing Collision Limit for the Spatially Homogeneous Boltzmann Equation