Year: 2018
Type: preprint
Abstract: We outline a new method of construction of global-in-time weak solutions of the Liouville equation - and also of the associated BBGKY hierarchy - corresponding to the hard sphere singular Hamiltonian. Our method makes use only of geometric reflection arguments on phase space. As a consequence of our method, in the case of $N=2$ hard spheres, we show for any chaotic initial data, the unique global-in-time weak solution $F$ of the Liouville equation is realised as $F=\mathsf{R}(f\otimes f)$ in the sense of tempered distributions on $T\mathbb{R}^{6}\times (-\infty, \infty)$, where $\mathsf{R}$ is a 'reflection-type' operator on Schwartz space, and $f$ is a global-in-time classical solution of the 1-particle free transport Liouville equation on $T\mathbb{R}^{3}$.
Source: arXiv (Cornell University)
Author: Wilkinson, Mark
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Gran Sasso Science Institute
OpenAlex ID: W2809965288