Velocity Decay Estimates for Boltzmann equation with hard potentials

Abstract

We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ($\gamma +2s>2$), under the assumption that the mass, energy, and entropy densities are bounded above, and the mass density is bounded below. These estimates are self-generating, i.e. they do not require corresponding decay assumptions on the initial data. Our results extend the recent work of Imbert-Mouhot-Silvestre (arXiv:1804.06135), which addressed the case of moderately soft potentials ($\gamma +2s\in [0,2]$).

16 pages

References in corpus (6)

• Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
• Global Strong Solutions of the Boltzmann Equation without Angular Cut-off
• Cooling process for inelastic Boltzmann equations for hard spheres, Part II: Self-similar solutions and tail behavior
• Factorization for non-symmetric operators and exponential H-theorem
• Decay estimates for large velocities in the Boltzmann equation without cutoff
• A new approach to the creation and propagation of exponential moments in the Boltzmann equation