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A remark on CannoneKarch solutions to the homogeneous Boltzmann equation for Maxwellian molecules
1.  Graduate School of Human and Environmental Studies, Kyoto University, Kyoto, 6068501, Japan 
References:
[1] 
R. Alexandre, L. Desvillettes, C. Villani and B. Wennberg, Entropy dissipation and longrange interactions, Arch. Rational Mech. Anal., 152 (2000), 327355. 
[2] 
R. Alexandre and M. El Safadi, LittlewoodPaley theory and regularity issues in Boltzmann homogeneous equations. I. Noncutoff and Maxwellian molecules, Math. Models Methods Appl. Sci., 15 (2005), 907920. 
[3] 
R. Alexandre, Y. Morimoto, S. Ukai, C.J. Xu and T. Yang, Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff, Kyoto J. Math., 52 (2012), 433463. 
[4] 
M. Cannone and G. Karch, Infinite energy solutions to the homogeneous Boltzmann equation, Comm. Pure Appl. Math., 63 (2010), 747778. doi: 10.1002/cpa.20298. 
[5] 
Z. H. Huo, Y. Morimoto, S. Ukai and T. Yang, Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff, Kinetic and Related Models, 1 (2008), 453489. 
[6] 
N. Jacob, "PseudoDifferential Operators and Markov Process. Vol. 1. Fourier Analysis and Semigroups," Imperial College Press, London, 2001. 
[7] 
Y. Morimoto, S. Ukai, C.J. Xu and T. Yang, Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff, Discrete and Continuous Dynamical Systems, 24 (2009), 187212. 
[8] 
H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Wahrsch. Verw. Geb., 46 (1978/79), 67105. doi: 10.1007/BF00535689. 
[9] 
G. Toscani and C. Villani, Probability metrics and uniqueness of the solution to the Boltzmann equations for Maxwell gas, J. Statist. Phys., 94 (1999), 619637. 
[10] 
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal., 143 (1998), 273307. 
[11] 
C. Villani, "A Review of Mathematical Topics in Collisional Kinetic Theory," in "Handbook of Mathematical Fluid Dynamics," Vol. I (eds. S. Friedlander and D. Serre), NorthHolland, Amsterdam, (2002), 71305. 
[12]  
[13] 
Y. Morimoto and T. Yang, Villani conjecture on smoothing effect of the homogeneous Boltzmann equation with measure initial datum, preprint. 
show all references
References:
[1] 
R. Alexandre, L. Desvillettes, C. Villani and B. Wennberg, Entropy dissipation and longrange interactions, Arch. Rational Mech. Anal., 152 (2000), 327355. 
[2] 
R. Alexandre and M. El Safadi, LittlewoodPaley theory and regularity issues in Boltzmann homogeneous equations. I. Noncutoff and Maxwellian molecules, Math. Models Methods Appl. Sci., 15 (2005), 907920. 
[3] 
R. Alexandre, Y. Morimoto, S. Ukai, C.J. Xu and T. Yang, Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff, Kyoto J. Math., 52 (2012), 433463. 
[4] 
M. Cannone and G. Karch, Infinite energy solutions to the homogeneous Boltzmann equation, Comm. Pure Appl. Math., 63 (2010), 747778. doi: 10.1002/cpa.20298. 
[5] 
Z. H. Huo, Y. Morimoto, S. Ukai and T. Yang, Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff, Kinetic and Related Models, 1 (2008), 453489. 
[6] 
N. Jacob, "PseudoDifferential Operators and Markov Process. Vol. 1. Fourier Analysis and Semigroups," Imperial College Press, London, 2001. 
[7] 
Y. Morimoto, S. Ukai, C.J. Xu and T. Yang, Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff, Discrete and Continuous Dynamical Systems, 24 (2009), 187212. 
[8] 
H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Wahrsch. Verw. Geb., 46 (1978/79), 67105. doi: 10.1007/BF00535689. 
[9] 
G. Toscani and C. Villani, Probability metrics and uniqueness of the solution to the Boltzmann equations for Maxwell gas, J. Statist. Phys., 94 (1999), 619637. 
[10] 
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations, Arch. Rational Mech. Anal., 143 (1998), 273307. 
[11] 
C. Villani, "A Review of Mathematical Topics in Collisional Kinetic Theory," in "Handbook of Mathematical Fluid Dynamics," Vol. I (eds. S. Friedlander and D. Serre), NorthHolland, Amsterdam, (2002), 71305. 
[12]  
[13] 
Y. Morimoto and T. Yang, Villani conjecture on smoothing effect of the homogeneous Boltzmann equation with measure initial datum, preprint. 
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