Hydrodynamic Limit of a Kinetic Gas Flow Past an Obstacle

Given an obstacle in 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 | → ∞ , which approaches the corresponding Navier–Stokes steady flow, as the mean-free path goe...

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Bibliographic Details
Published inCommunications in mathematical physics Vol. 364; no. 2; pp. 765 - 823
Main Authors Esposito, R., Guo, Y., Marra, R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2018
Springer Nature B.V
Subjects
Classical and Quantum Gravitation
Complex Systems
Distribution functions
Fluid dynamics
Fluid flow
Gas flow
Mathematical and Computational Physics
Mathematical Physics
Navier-Stokes equations
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Steady flow
Theoretical
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Summary:Given an obstacle in 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 | → ∞ , 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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-018-3173-1