The Boltzmann equation evolves a particle density by free motion and binary collisions,
where
is the Boltzmann collision integral.
Its precise collision kernel specifies the interaction law. Classical smooth solutions
and weaker distributional or renormalized solutions are different solution classes.
The Boltzmann-Grad limit asks when dilute
microscopic particle systems converge to this kinetic equation.
Bodineau, T.; Gallagher, I.; Saint-Raymond, L.; and Simonella, S. "Fluctuation Theory in the Boltzmann-Grad Limit." J. Stat. Phys.180,
873-895, 2020. https://doi.org/10.1007/s10955-020-02549-5.DiPerna,
R. J. and Lions, P.-L. "On the Cauchy Problem for Boltzmann Equations:
Global Existence and Weak Stability." Ann. Math.130, 321-366,
1989. https://doi.org/10.2307/1971423.
by free motion and binary collisions,
is the Boltzmann collision integral.
Its precise collision kernel specifies the interaction law. Classical smooth solutions
and weaker distributional or renormalized solutions are different solution classes.
The Boltzmann-Grad limit asks when dilute
microscopic particle systems converge to this kinetic equation.
