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On the Boltzmann equation, quantitative studies and hydrodynamical limits 10.17863/CAM.16234 Briant, Marc The present thesis deals with the mathematical treatment of kinetic theory and focuses more precisely on the Boltzmann equation. We investigate several properties of the solutions to the latter equation: their positivity and their hydrodynamical limits for instance. We also study the local Cauchy problem for a quantic version of the Boltzmann equation. University of Cambridge 2014-11-11 Thesis Doctoral Doctor of Philosophy (PhD) en This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/H023348/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis. https://www.repository.cam.ac.uk/handle/1810/246471 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/a2e44c45-caf3-4537-85c7-bc676706dda9/download 835269bda140c10400fe0606a14c3d21 https://apollo8-f-pro.lib.cam.ac.uk/bitstreams/c5a2774e-1b13-49f0-ba26-65ef49183713/download 25cae5336785d29955a0f374625db504 https://www.rioxx.net/licenses/all-rights-reserved/ Boltzmann equation Hydrodynamical limit Boltzmann-Nordheim equation