Small Data Global Well-Posedness for a Boltzmann Equation via Bilinear Spacetime Estimates

We provide a new analysis of the Boltzmann equation with constant collision kernel in two space dimensions. The scaling-critical Lebesgue is $$L^2_{x,v}$$ ; we prove global well-posedness and version scattering, assuming that data $$f_0$$ sufficiently smooth localized, norm small. proof relies upon bilinear spacetime estimate for “gain” term Boltzmann’s equation, combined novel application Kaniel–Shinbrot iteration.