Global existence proofs for the Boltzmann equation

The Boltzmann equation has occupied a dominant position in the study of gas dynamics over the last 110 years. However, no global existence theorem of any sort was proved prior to the last ten years for the spatially inhomogeneous equation. The present investigation is concerned with a review of the literature on global existence theorems for the Boltzmann equation, taking into account developments from the earliest results obtained by Carleman (1933) to the recent perturbation theorems. Attention is given to the spatially homogeneous equation, the Boltzmann equation with mollifier, the development of local existence proofs for the spatially dependent equations, and global existence near equilibrium.