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arXiv · 1702.05656

Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle

Raffaele Esposito·Yan Guo·Rossana Marra
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Abstract

Given an obstacle in $\mathbb{R}^3$ and a non-zero velocity with small amplitude at the infinity, we construct the unique steady Boltzmann solution flowing around such an obstacle with the prescribed velocity as $|x|\to \infty$, which approaches the corresponding Navier-Stokes steady flow, as the mean-free path goes to zero. Furthermore, we establish the error estimate between the Boltzmann solution and its Navier-Stokes approximation. Our method consists of new $L^6$ and $L^3$ estimates in the unbounded exterior domain, as well as an iterative scheme preserving the positivity of the distribution function.

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Raffaele Esposito, Yan Guo, Rossana Marra. 2017-02-18. Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle. https://doi.org/10.1007/s00220-018-3173-1

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