caa a22 4500 605516006 CHVBK 20210128100712.0 cr unu---uuuuu 210128e20151101xx s 000 0 eng 10.1007/s00205-015-0874-x doi (NATIONALLICENCE)springer-10.1007/s00205-015-0874-x Briant M. Centre for Mathematical Sciences, University of Cambridge DPMMS, Wilberforce Road, CB3 0WA, Cambridge, UK aut Instantaneous Filling of the Vacuum for the Full Boltzmann Equation in Convex Domains [Elektronische Daten] [M. Briant] We prove the immediate appearance of a lower bound for mild solutions to the full Boltzmann equation in the torus or a C 2 convex domain with specular boundary conditions, under the sole assumption of continuity away from the grazing set of the solution. These results are entirely constructive if the domain is C 3 and strictly convex. We investigate a wide range of collision kernels, some satisfying Grad's cutoff assumption and others not. We show that this lower bound is exponential, independent of time and space with explicit constants depending only on the a priori bounds on the solution. In particular, this lower bound is Maxwellian in the case of cutoff collision kernels. A thorough study of characteristic trajectories, as well as a geometric approach of grazing collisions against the boundary are derived. Springer-Verlag Berlin Heidelberg, 2015 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 985-1041 0003-9527 218:2<985 2015 218 205 https://doi.org/10.1007/s00205-015-0874-x text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0874-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Briant M. Centre for Mathematical Sciences, University of Cambridge DPMMS, Wilberforce Road, CB3 0WA, Cambridge, UK aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/2(2015-11-01), 985-1041 0003-9527 218:2<985 2015 218 205