Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle

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.

Corrected some omissions

References in corpus (2)

• Stationary solutions to the Boltzmann equation in the Hydrodynamic limit
• Geometric Correction for Diffusive Expansion of Steady Neutron Transport Equation

Cited by in corpus (6)

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• Small Knudsen rate of convergence to rarefaction wave for the Landau equation
• Diffusive limit for a Boltzmann-like equation with non-conserved momentum
• Strong diffusive limit of the Boltzmann equation with Maxwell boundary condition
• Asymptotic Analysis of Boltzmann Equation in Bounded Domains
• Hydrodynamic limit of the Boltzmann equation to the planar rarefaction wave in three dimensional space