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On Global-in-time Chaotic Weak Solutions of the Liouville Equation for Hard Spheres. (arXiv:1807.01017v1 [math.AP])
来源于:arXiv
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
$T\mathbb{R}^{3}$. 查看全文>>