We present nonlinear functionals measuring physical space variation and L1-distance between two classical solutions for the Boltzmann equation with a cut-off inverse power potential. In the case that initial datum is a small, smooth perturbation of vacuum and decays fast enough in the phase space, we show that these functionals satisfy stability estimates which lead to BV-type estimates and a uniform L1-stability. © 2004 Elsevier Inc. All rights reserved.
Ha, S. Y. (2005). Nonlinear functionals of the Boltzmann equation and uniform stability estimates. Journal of Differential Equations, 215(1), 178–205. https://doi.org/10.1016/j.jde.2004.07.022