Julio Cisneros Lorduy, The Cauchy Problem for the Elastic Boltzmann Equation with an External Force, Journal of Modern Mathematics and Statistics, Volume 14,Issue 1, 2020, Pages 10-14, ISSN 1994-5388, jmmstat.2020.10.14, (https://makhillpublications.co/view-article.php?doi=jmmstat.2020.10.14) Abstract: The Cauchy problem for the elastic Boltzmann equation with external force is considered for near vacuum data. We prove the existence of solutions for initial data small enough with respect to the sup norm by using the fixed point theorem of Krasnoselskii. Keywords: Boltzmann equation;kinetic theory;fixed point;enough;sup norm;Cauchy problem