Renormalized Boltzmann solution

A weak solution framework in which a suitable nonlinear transform $\beta (f)$ satisfies a transport equation with transformed collision source ${\beta }^{\prime }(f)Q(f,f)$, interpreted with the required integrability and possible framework-dependent defect terms. Renormalization addresses distributions whose raw collision term is not integrable enough to support the ordinary weak formulation. This is different from a classical smooth solution and does not by itself imply smooth global well-posedness.