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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), 327. Google Scholar 
[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), 907. Google Scholar 
[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), 433. Google Scholar 
[4] 
M. Cannone and G. Karch, Infinite energy solutions to the homogeneous Boltzmann equation,, Comm. Pure Appl. Math., 63 (2010), 747. doi: 10.1002/cpa.20298. Google Scholar 
[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), 453. Google Scholar 
[6] 
N. Jacob, "PseudoDifferential Operators and Markov Process. Vol. 1. Fourier Analysis and Semigroups,", Imperial College Press, (2001). Google Scholar 
[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), 187. Google Scholar 
[8] 
H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules,, Wahrsch. Verw. Geb., 46 (): 67. doi: 10.1007/BF00535689. Google Scholar 
[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), 619. Google Scholar 
[10] 
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations,, Arch. Rational Mech. Anal., 143 (1998), 273. Google Scholar 
[11] 
C. Villani, "A Review of Mathematical Topics in Collisional Kinetic Theory,", in, (2002), 71. Google Scholar 
[12] 
C. Villani, private communication,, Kyoto, (2008). Google Scholar 
[13] 
Y. Morimoto and T. Yang, Villani conjecture on smoothing effect of the homogeneous Boltzmann equation with measure initial datum,, preprint., (). Google Scholar 
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), 327. Google Scholar 
[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), 907. Google Scholar 
[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), 433. Google Scholar 
[4] 
M. Cannone and G. Karch, Infinite energy solutions to the homogeneous Boltzmann equation,, Comm. Pure Appl. Math., 63 (2010), 747. doi: 10.1002/cpa.20298. Google Scholar 
[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), 453. Google Scholar 
[6] 
N. Jacob, "PseudoDifferential Operators and Markov Process. Vol. 1. Fourier Analysis and Semigroups,", Imperial College Press, (2001). Google Scholar 
[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), 187. Google Scholar 
[8] 
H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules,, Wahrsch. Verw. Geb., 46 (): 67. doi: 10.1007/BF00535689. Google Scholar 
[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), 619. Google Scholar 
[10] 
C. Villani, On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations,, Arch. Rational Mech. Anal., 143 (1998), 273. Google Scholar 
[11] 
C. Villani, "A Review of Mathematical Topics in Collisional Kinetic Theory,", in, (2002), 71. Google Scholar 
[12] 
C. Villani, private communication,, Kyoto, (2008). Google Scholar 
[13] 
Y. Morimoto and T. Yang, Villani conjecture on smoothing effect of the homogeneous Boltzmann equation with measure initial datum,, preprint., (). Google Scholar 
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