Short-time Green function for Boltzmann and Landau Equations
アブストラクト
We develop a short-time pointwise Green-function theory for variable-coefficient kinetic equations with a nonnegative Hölder background. We first construct the small-jump Green function by freezing coefficients along kinetic characteristics and then recover the full kernel through a convergent parametrix expansion. The resulting bounds capture the fractional Kolmogorov geometry near characteristics and rapid decay away from them, providing the analytic foundation for the scaling-critical theory. This is a joint work with Ke Chen and Quoc-Hung Nguyen.