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Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals
Acoustic limit of the Boltzmann equation: Classical solutions
1. | Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York City, NY 10012 |
$\partial_t F_\varepsilon +\v$•$grad$x$F_\varepsilon =\frac{1}{\varepsilon} \Q(F_\varepsilon,F_\varepsilon)\,$
inside a periodic box $\mathbb{T}^3$, we establish the global-in-time uniform energy estimates of $f_\varepsilon$ in $\varepsilon$ and prove that $f_\varepsilon$ converges strongly to $f$ whose dynamics is governed by the acoustic system. The collision kernel $\Q$ includes hard-sphere interaction and inverse-power law with an angular cutoff.
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