On Measure Solutions of the Boltzmann Equation part I: Moment Production and Stability Estimates

Xuguang Lu (1) , Clément Mouhot (2)

1 Department of Mathematical Sciences
2 DPMMS - Department of Pure Mathematics and Mathematical Statistics

The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. Moment production estimates in the usual form and in the exponential form are obtained for measure solutions with and without angular cutoff on the collision kernel. For the Grad angular cutoff, it is also established the strong stability estimate for measure solutions.

Mots clés: Boltzmann equation; spatially homogeneous; measure solution; moment estimate; moment production; exponential moment; stability estimate; Mehler transform

Domaines: Equations aux dérivées partielles [math.AP]

Xuguang Lu, Clément Mouhot. On Measure Solutions of the Boltzmann Equation part I: Moment Production and Stability Estimates. 2011. ⟨hal-00561793v1⟩