| Abstract: |
| In this talk, we discuss the asymptotic behavior of a rarefied flow, governed by the Boltzmann equation, in the weakly nonlinear regime where both the Reynolds number and the Knudsen number are small. Specifically, we first address boundary-value problems of the Boltzmann equation and apply the Hilbert expansion for small Knudsen numbers (i.e., scaled mean free path) to derive a fluid-dynamic system in the case where the Reynolds number is of the same order as the Knudsen number. Using the matched asymptotic expansion, this system is then applied to analyze the flow past a sphere, providing insights into gas behavior around the sphere. In particular, we derive a drag formula that accounts for both rarefaction and inertia effects as well as their coupling. The work is in collaboration with Yuki Tatsudani and Tetsuro Tsuji. |
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