caa a22 4500 605496064 CHVBK 20210128100534.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10231-014-0440-4 doi (NATIONALLICENCE)springer-10.1007/s10231-014-0440-4 Dolera Emanuele Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via Campi 213/b, 41125, Modena, Italy aut Mathematical treatment of the homogeneous Boltzmann equation for Maxwellian molecules in the presence of singular kernels [Elektronische Daten] [Emanuele Dolera] This paper proves the existence of weak solutions to the the spatially homogeneous Boltzmann equation for Maxwellian molecules, when the initial data are chosen from the space of all Borel probability measures on $$\mathbb {R}^3$$ R 3 with finite second moments, and the (angular) collision kernel satisfies a very weak cutoff condition, namely $$\int _{-1}^{1} x^2 b(x) \mathrm {d}x < +\infty $$ ∫ - 1 1 x 2 b ( x ) d x < + ∞ . For the equation at issue, the uniqueness of the solution corresponding to a specific initial datum has been recently established in Fournier and Guérin (J Stat Phys 131:749-781, 2008). Finally, conservation of momentum and energy is also proved for these weak solutions, without resorting to any boundedness of the entropy. Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg, 2014 Boltzmann equation nationallicence Maxwellian molecules nationallicence Moments nationallicence Sum of random variables nationallicence Uniform integrability nationallicence Very weak cutoff nationallicence Weak solution nationallicence Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1707-1732 0373-3114 194:6<1707 2015 194 10231 https://doi.org/10.1007/s10231-014-0440-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10231-014-0440-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Dolera Emanuele Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università di Modena e Reggio Emilia, via Campi 213/b, 41125, Modena, Italy aut NATIONALLICENCE 773 0- Annali di Matematica Pura ed Applicata (1923 -) Springer Berlin Heidelberg 194/6(2015-12-01), 1707-1732 0373-3114 194:6<1707 2015 194 10231