Uniform L1L1-stability estimate of the Boltzmann equation near a local Maxwellian

We consider the Boltzmann equation describing the spacial–temporal evolution of the velocity distribution function in a near exponential local Maxwellian regime. We present two robust nonlinear functionals measuring possible future collisions and L1L1-distance between two mild solutions. Through the explicit local cancellation of the collision mechanism due to the special structure of an exponential local Maxwellian solution, we show that the nonlinear functionals in [S.-Y. Ha, Nonlinear functionals of the Boltzmann equation and uniform stability estimates, J. Differential Equations 215 (2005) 178–205] satisfy uniform stability estimates. These functionals can be employed to the study of L1L1-scattering and uniform L1L1-stability estimate of mild solutions for the Boltzmann equation with inverse power intermolecular potentials.