R. Alexandre, L. Desvillettes, C. Villani, and B. Wennberg, Entropy Dissipation and Long-Range Interactions, Archive for Rational Mechanics and Analysis, vol.152, issue.4, pp.327-355, 2000.
DOI : 10.1007/s002050000083
URL : http://www.cmla.ens-cachan.fr/Cmla/Publications/2000/CMLA2000-21.ps.gz

R. Alexandre, Y. Morimoto, S. Ukai, C. Xu, and T. Yang, Uncertainty principle and kinetic equations, Journal of Functional Analysis, vol.255, issue.8, pp.2013-2066, 2008.
DOI : 10.1016/j.jfa.2008.07.004
URL : https://hal.archives-ouvertes.fr/hal-00435676

R. Alexandre and C. Villani, On the Boltzmann equation for long-range interactions, Communications on Pure and Applied Mathematics, vol.139, issue.1, pp.30-70, 2002.
DOI : 10.1007/s002050050054

R. Alexandre and M. Safadi, LITTLEWOOD???PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES, Mathematical Models and Methods in Applied Sciences, vol.10, issue.06, pp.907-920, 2005.
DOI : 10.1007/s002050050106

R. Alexandre and M. Elsafadi, Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations. II. Non cutoff case and non Maxwellian molecules, Discrete Contin. Dyn. Syst, vol.24, issue.1, pp.1-11, 2009.

R. Alexandre, Y. Morimoto, S. Ukai, C. Xu, and T. Yang, Regularizing Effect and Local Existence for the Non-Cutoff Boltzmann Equation, Archive for Rational Mechanics and Analysis, vol.143, issue.1, pp.39-123, 2010.
DOI : 10.1016/j.matpur.2007.03.003
URL : https://hal.archives-ouvertes.fr/hal-01116729

R. Alonso, J. A. Cañizo, I. Gamba, and C. Mouhot, A New Approach to the Creation and Propagation of Exponential Moments in the Boltzmann Equation, Communications in Partial Differential Equations, vol.5, issue.1, pp.155-169, 2013.
DOI : 10.1007/BF02183613
URL : https://hal.archives-ouvertes.fr/hal-00677951

R. Alonso, I. M. Gamba, and M. Taskovi´ctaskovi´c, Exponentially-tailed regularity and time asymptotic for the homogeneous Boltzmann equation, 2017.

A. V. Bobylev, Moment inequalities for the boltzmann equation and applications to spatially homogeneous problems, Journal of Statistical Physics, vol.33, issue.100, pp.5-61183, 1997.
DOI : 10.1063/1.529578

A. V. Bobylev, I. M. Gamba, and V. A. Panferov, Moment Inequalities and High-Energy Tails for Boltzmann Equations with Inelastic Interactions, Journal of Statistical Physics, vol.116, issue.5/6, pp.5-61651, 2004.
DOI : 10.1023/B:JOSS.0000041751.11664.ea
URL : http://arxiv.org/pdf/math-ph/0306014

V. Alexander, I. M. Bobylev, and . Gamba, Upper Maxwellian bounds for the Boltzmann equation with pseudo-Maxwell molecules, Kinet. Relat. Models, vol.10, issue.3, pp.573-585, 2017.

M. Briant, Instantaneous Filling of the Vacuum for the Full Boltzmann Equation in Convex Domains, Archive for Rational Mechanics and Analysis, vol.234, issue.3, pp.985-1041, 2015.
DOI : 10.1007/s00220-002-0777-1
URL : https://hal.archives-ouvertes.fr/hal-01492021

M. Briant, Instantaneous exponential lower bound for solutions to the Boltzmann equation with Maxwellian diffusion boundary conditions, Kinetic and Related Models, vol.8, issue.2, pp.281-308, 2015.
DOI : 10.3934/krm.2015.8.281
URL : https://hal.archives-ouvertes.fr/hal-01492036

M. Briant and A. Einav, On the Cauchy Problem for the Homogeneous Boltzmann???Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments, Journal of Statistical Physics, vol.239, issue.10, pp.1108-1156, 2016.
DOI : 10.1016/S1874-5792(02)80004-0
URL : https://hal.archives-ouvertes.fr/hal-01492026

S. Cameron, L. Silvestre, and S. Snelson, Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials, Annales de l'Institut Henri Poincar?? C, Analyse non lin??aire, vol.35, issue.3, 2017.
DOI : 10.1016/j.anihpc.2017.07.001

C. Cercignani, The Boltzmann equation and its applications, of Applied Mathematical Sciences, 1988.
DOI : 10.1007/978-1-4612-1039-9

P. Constantin and V. Vicol, Nonlinear maximum principles for dissipative linear nonlocal operators and applications, Geometric and Functional Analysis, vol.27, issue.3, pp.1289-1321, 2012.
DOI : 10.1016/j.anihpc.2009.11.006
URL : http://arxiv.org/pdf/1110.0179

L. Desvillettes, Some applications of the method of moments for the homogeneous Boltzmann and Kac equations, Archive for Rational Mechanics and Analysis, vol.5, issue.4, pp.387-404, 1993.
DOI : 10.1007/BF00375586

L. Desvillettes and C. Mouhot, Large time behavior of the a priori bounds for the solutions to the spatially homogeneous Boltzmann equations with soft potentials, Asymptot. Anal, vol.54, pp.3-4235, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00079949

L. Desvillettes and C. Mouhot, Stability and Uniqueness for the Spatially Homogeneous Boltzmann Equation with Long-Range Interactions, Archive for Rational Mechanics and Analysis, vol.19, issue.3???4, pp.227-253, 2009.
DOI : 10.1080/03605309408821082
URL : https://hal.archives-ouvertes.fr/hal-00079713

L. Desvillettes and B. Wennberg, Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff, Communications in Partial Differential Equations, vol.45, issue.1-2, pp.133-155, 2004.
DOI : 10.1080/03605309408821082

R. J. Diperna and P. Lions, On the Cauchy Problem for Boltzmann Equations: Global Existence and Weak Stability, The Annals of Mathematics, vol.130, issue.2, pp.321-366, 1989.
DOI : 10.2307/1971423

T. Elmroth, Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range, Archive for Rational Mechanics and Analysis, vol.5, issue.1, pp.1-12, 1983.
DOI : 10.1007/BF00251722

F. Filbet and C. Mouhot, Analysis of spectral methods for the homogeneous Boltzmann equation, Transactions of the American Mathematical Society, vol.363, issue.04, pp.1947-1980, 2011.
DOI : 10.1090/S0002-9947-2010-05303-6
URL : https://hal.archives-ouvertes.fr/hal-00339426

I. M. Gamba, V. Panferov, and C. Villani, Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation, Archive for Rational Mechanics and Analysis, vol.95, issue.1???2, pp.253-282, 2009.
DOI : 10.1023/A:1004546031908

M. Irene, N. Gamba, M. Pavlovi´cpavlovi´c, and . Taskovi´ctaskovi´c, On pointwise exponentially weighted estimates for the Boltzmann equation, 2017.

C. Francois¸golsefrancois¸francois¸golse, C. Imbert, A. F. Mouhot, and . Vasseur, Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation, 2017.

M. P. Gualdani, S. Mischler, and C. Mouhot, Factorization for non-symmetric operators and exponential h-theorem, 2018.
URL : https://hal.archives-ouvertes.fr/hal-00495786

C. Henderson and S. Snelson, C ? smoothing for weak solutions of the inhomogeneous Landau equation, 2017.

C. Henderson, S. Snelson, and A. Tarfulea, Local existence, lower mass bounds, and smoothing for the Landau equation, 2017.

Z. Huo, Y. Morimoto, S. Ukai, and T. Yang, Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff, Kinet. Relat. Models, vol.1, issue.3, pp.453-489, 2008.

E. Ikenberry and C. Truesdell, On the Pressures and the Flux of Energy in a Gas according to Maxwell's Kinetic Theory, I, Indiana University Mathematics Journal, vol.5, issue.1, pp.1-54, 1956.
DOI : 10.1512/iumj.1956.5.55001

C. Imbert and L. Silvestre, Weak Harnack inequality for the Boltzmann equation without cut-off, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01357047

X. Lu, Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation, J. Statist. Phys, vol.96, pp.3-4765, 1999.

X. Lu and C. Mouhot, On measure solutions of the Boltzmann equation, part I: Moment production and stability estimates, Journal of Differential Equations, vol.252, issue.4, pp.3305-3363, 2012.
DOI : 10.1016/j.jde.2011.10.021
URL : https://hal.archives-ouvertes.fr/hal-00561793

J. C. Maxwell, On the Dynamical Theory of Gases, Philosophical Transactions of the Royal Society of London, vol.157, issue.0, pp.49-88, 1867.
DOI : 10.1098/rstl.1867.0004

S. Mischler and C. Mouhot, Cooling Process for Inelastic Boltzmann Equations for Hard Spheres, Part II: Self-Similar Solutions and Tail Behavior, Journal of Statistical Physics, vol.19, issue.2-4, pp.2-4703, 2006.
DOI : 10.1093/acprof:oso/9780198530381.001.0001
URL : https://hal.archives-ouvertes.fr/hal-00087235

S. Mischler and B. Wennberg, On the spatially homogeneous Boltzmann equation, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.16, issue.4, pp.467-501, 1999.
DOI : 10.1016/S0294-1449(99)80025-0
URL : https://doi.org/10.1016/s0294-1449(99)80025-0

Y. Morimoto, S. Ukai, C. Xu, and T. Yang, Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff, Discrete Contin. Dyn. Syst, vol.24, issue.1, pp.187-212, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00434249

C. Mouhot, Quantitative Lower Bounds for the Full Boltzmann Equation, Part I: Periodic Boundary Conditions, Communications in Partial Differential Equations, vol.282, issue.5-6, pp.881-917, 2005.
DOI : 10.1007/s00220-002-0777-1
URL : https://hal.archives-ouvertes.fr/hal-00087249

A. Ja and . Povzner, On the Boltzmann equation in the kinetic theory of gases, Mat. Sb. (N.S.), vol.58, issue.100, pp.65-86, 1962.

L. Silvestre, A New Regularization Mechanism for the Boltzmann Equation Without Cut-Off, Communications in Mathematical Physics, vol.1, issue.4, pp.69-100, 2016.
DOI : 10.1016/S1874-5792(02)80004-0

L. Silvestre, Upper bounds for parabolic equations and the Landau equation, Journal of Differential Equations, vol.262, issue.3, pp.3034-3055, 2017.
DOI : 10.1016/j.jde.2016.11.010

C. Villani, A Review of Mathematical Topics in Collisional Kinetic Theory, Handbook of mathematical fluid dynamics, pp.71-305, 2002.
DOI : 10.1016/S1874-5792(02)80004-0

B. Wennberg, The Povzner inequality and moments in the Boltzmann equation, Proceedings of the VIII International Conference on Waves and Stability in Continuous Media number 45, part II, pp.673-681, 1995.