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

M. Bennoune, M. Lemou, and L. Mieussens, Uniformly stable numerical schemes for the Boltzmann equation preserving the compressible Navier???Stokes asymptotics, Journal of Computational Physics, vol.227, issue.8, pp.3781-3803, 2008.
DOI : 10.1016/j.jcp.2007.11.032
URL : https://hal.archives-ouvertes.fr/hal-00348598

G. Bird, Molecular gas dynamics and the direct simulation of gas flows, 1994.

A. Bobylev, Exact solutions of the Boltzmann equation, Akademiia Nauk SSSR Doklady, pp.1296-1299, 1975.

A. Bobylev, The theory of the nonlinear spatially uniform Boltzmann equation for Maxwell molecules, Soviet Sci. Rev. Sect. C: Math. Phys, vol.7, pp.111-233, 1988.

A. Bobylev, A. Palczewski, and J. Schneider, On approximation of the Boltzmann equation by discrete velocity models, Comptes rendus de l'Académie des sciences, Mathématique, vol.1, issue.3205, pp.639-644, 1995.

A. Bobylev and S. Rjasanow, Difference scheme for the Boltzmann equation based on fast fourier transform, 1996.

L. Boltzmann, Weitere studienüberstudien¨studienüber das wärmegleichgewicht unter gas-molekülen, pp.275-370
DOI : 10.1017/cbo9781139381420.023

C. Buet, S. Cordier, and P. Degond, Regularized Boltzmann operators, Computers & Mathematics with Applications, vol.35, issue.1-2, pp.55-74, 1998.
DOI : 10.1016/S0898-1221(97)00258-7
URL : http://doi.org/10.1016/s0898-1221(97)00258-7

Z. Cai, Y. Fan, and L. Ying, Entropy monotonic spectral method for Boltzmann equation, 2017.

C. Cercignani, The Boltzmann equation and its applications, Applied Mathematical Sciences, vol.67, 1988.
DOI : 10.1007/978-1-4612-1039-9

L. Desvillettes, Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules, Transport Theory and Statistical Physics, vol.34, issue.3, pp.341-357, 1997.
DOI : 10.1080/03605309408821082

L. Desvillettes, Regularization for the non Cutoff 2D Radially Symmetric Boltzmann Equation with a Velocity Dependant Cross Section, Transport Theory and Statistical Physics, vol.25, pp.3-5, 1996.

L. Desvillettes, F. Golse, R. Brun, R. Campargue, and R. , On the Smoothing Properties of a Model Boltzmann Equation without Grad's Cutoff Assumption, Proceedings of the 21st International Symposium on Rarefied Gas Dynamics, pp.47-54, 1999.

L. Desvillettes and F. Golse, On a Model Boltzmann Equation without Angular Cutoff, Differential and Integral Equations, pp.4-6, 2000.

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

G. Dimarco and L. Pareschi, High order asymptotic-preserving schemes for the Boltzmann equation, Comptes Rendus Mathematique, vol.350, issue.9-10, pp.9-10, 2012.
DOI : 10.1016/j.crma.2012.05.010
URL : https://hal.archives-ouvertes.fr/hal-00933518

G. Dimarco and L. Pareschi, Asymptotic Preserving Implicit-Explicit Runge--Kutta Methods for Nonlinear Kinetic Equations, SIAM Journal on Numerical Analysis, vol.51, issue.2, pp.1064-1087, 2013.
DOI : 10.1137/12087606X
URL : https://hal.archives-ouvertes.fr/hal-00966062

G. Dimarco and L. Pareschi, Numerical methods for kinetic equations, Acta Numerica, pp.369-520, 2014.
DOI : 10.1017/s0962492914000063

E. Dolera, On the spectrum of the linearized Boltzmann collision operator for Maxwellian molecules, Boll. UMI, vol.46, pp.67-105, 2010.

I. M. Gamba-;-j, C. D. Haack, J. Hauck, and . Hu, A fast spectral method for the Boltzmann collision operator with general collision kernels, SIAM J. for Scientific Computing, 2017.

D. Goldstein, J. Sturtevant, and . Broadwell, Investigations of the motion of discrete-velocity gases, Progress in Astronautics and Aeronautics, pp.100-117, 1989.

P. Gressman and R. Strain, Global classical solutions of the Boltzmann equation without angular cut-off, Journal of the American Mathematical Society, vol.24, issue.3, pp.771-847, 2011.
DOI : 10.1090/S0894-0347-2011-00697-8

S. Jin, Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms, Journal of Computational Physics, vol.122, issue.1, pp.51-67, 1995.
DOI : 10.1006/jcph.1995.1196
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.1196

S. Jin, Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations, SIAM Journal on Scientific Computing, vol.21, issue.2, pp.441-454, 1999.
DOI : 10.1137/S1064827598334599
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.53.2629

S. Jin, Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations, a review, Riv. Math. Univ. Parma (N.S.), vol.3, issue.2, pp.177-216, 2012.

M. Krook and T. T. Wu, Exact solutions of the Boltzmann equation, The Physics of Fluids, pp.1589-1595, 1977.

N. Lerner, Y. Morimoto, K. Pravda-starov, and C. Xu, Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators, Kinetic and Related Models, vol.6, issue.3, pp.625-648, 2013.
DOI : 10.3934/krm.2013.6.625
URL : https://hal.archives-ouvertes.fr/hal-01116722

N. Lerner, Y. Morimoto, K. Pravda-starov, and C. Xu, Spectral and phase space analysis of the linearized non-cutoff Kac collision operator, Journal de Math??matiques Pures et Appliqu??es, vol.100, issue.6, pp.832-867, 2013.
DOI : 10.1016/j.matpur.2013.03.005
URL : https://hal.archives-ouvertes.fr/hal-01116721

N. Lerner, Y. Morimoto, K. Pravda-starov, and C. Xu, Gelfand???Shilov smoothing properties of the radially symmetric spatially homogeneous Boltzmann equation without angular cutoff, Journal of Differential Equations, vol.256, issue.2, pp.797-831, 2014.
DOI : 10.1016/j.jde.2013.10.001
URL : https://hal.archives-ouvertes.fr/hal-01116715

C. Mouhot and L. Pareschi, Fast algorithms for computing the Boltzmann collision operator, Mathematics of Computation, vol.75, issue.256, pp.1833-1852, 2006.
DOI : 10.1090/S0025-5718-06-01874-6
URL : https://hal.archives-ouvertes.fr/hal-00087285

V. A. Panferov and A. G. Heintz, A new consistent discrete-velocity model for the Boltzmann equation, Mathematical Methods in the Applied Sciences, vol.20, issue.7, pp.571-593, 2002.
DOI : 10.1007/978-1-4613-8566-0

L. Pareschi and B. Perthame, A Fourier spectral method for homogeneous boltzmann equations, Transport Theory and Statistical Physics, vol.52, issue.3-5, pp.369-382, 1996.
DOI : 10.1103/PhysRevLett.36.1107

L. Pareschi and G. Russo, Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator, SIAM Journal on Numerical Analysis, vol.37, issue.4, pp.1217-1245, 2000.
DOI : 10.1137/S0036142998343300

F. Rogier and J. Schneider, A direct method for solving the Boltzmann equation, Transport Theory and Statistical Physics, vol.23, issue.1-3, pp.313-338, 1994.
DOI : 10.1080/00411459408203868
URL : https://hal.archives-ouvertes.fr/hal-01313796

C. Villani, On a New Class of Weak Solutions to the Spatially Homogeneous Boltzmann and Landau Equations, Archive for Rational Mechanics and Analysis, vol.187, issue.Ser.2, pp.273-307, 1998.
DOI : 10.1103/PhysRev.187.382

C. Villani, A review of mathematical topics in collisional kinetic theory, Handbook of mathematical fluid dynamics, pp.71-74, 2002.