Journal of Statistical Physics, Vol. 123, No. 4, May 2006. p. 753-762.
DOI: 10.1007/s10955-006-9115-x
The definition of the concept of weak solution of the nonlinear Boltzmann equation, recently introduced by the author, is used to prove that, without any cutoff in the collision kernel, the Boltzmann equation for Maxwell molecules in the one-dimensional case has a global weak solution in this sense. Global conservation of energy follows.